Making one for $50 with those features is going to be difficult. Here is my very simple one:

It's made from MDF and some strips of wood, held together with some glue and wood screws. A sheet of ordinary window glass rests on the upper wood strips.
I used standard 12" fluorescent light fittings, disassembled, with the tubes replaced by UV tubes. They are connected to a piece of mains cable and a mains plug.
I time the exposure (11 minutes) with the kitchen timer on my Dell Streak tablet. Although it's very crude, I get excellent results - 8/8 mil tracks if necessary - with transparencies printed on my cheap inkjet printer.
It cost me the equivalent of about $40.
You could build a basic unit like mine, and add the bells and whistles later.
Some members of the Homebrew PCB Yahoo group are using UV LEDs, but they are far more expensive than a couple of UV tubes. Enough LEDs for a small board could cost over $100, IIRC.
The following is based on
Personal experience and extensive reading of the relevant literature after my wife burned her eyes with a UV germicidal lamp after following my instructions.
Test advice from Nichia re blue light hazard from visible white LEDs
You'd want a proper datasheet and the following is definitely on an "all care no responsibility" & this is my semi-informed opinion only basis, but:
EXPECTATIONS
(1) You'd want to exercise due care when using it on the bench - staring directly at the LED from close range would almost certainly produce a slow but noticeable amount of damage BUT this would probably take hours of exposure to manifest and I'd say almost certainly not less than minutes AND it would manifest as itchy or somewhat sore eyes and would self heal in about a week with no permanent damage.
(2) My real expectation is that you could play around with one of these as much as you wished while setting it up including looking into it across a model from the far side occasionally - and have no noticeable effect whatsoever.
(3) Even worst case you could probably not cause any sort of significant long term damage with anything you would sensibly do with it.
(4) If illuminating a largish area compared to the LED (eg a model) and having it fluoresce and reradiate visibly I'd expect the amount of UV to be at a very safe level.
Reasons to follow
Brief update - more to follow:
REASONS
I understand Kortuk's concern.
I believe that my advice as given is OK (read carefully please) BUT erring on the safe side is always wise.
(1) Background: UV and "arc-eye" & "snow blindness":
People exposed to bright high altitude sunlight for many hours risk being burned by the UV component of the sunlight. A skier at say 6000 feet above sea level who skis all day on a bright day without using eye protection has a good chance of experiencing a degree of "snow blindness". The eyes become itchy and somewhat inflamed. The UV has caused burning if the eye interior - mainly towards the surface. Even people who are exposed so badly that they are literally "blinded" and lose the practical use of their eyes due to soreness and inflammation, will essentially always recover without any permanent effects. Recovery is usually in under a week in typical cases. I've personally experienced minor "snow blindness" on a few past occasions either while skiing or in other higher altitude situations. Wearing eye protection makes much sense.
An identical effect occurs from looking at the arc when arc welding. Large quantities of emitted UV cause "arc-eye" - same result, different name.
Germicidal lamps which emit short wavelength UV
In my workshop I have a ~= 20 Watt UV germicidal lamp - in the form of a "fluorescent tube" BUT with no phosphor so no fluorescence just hard short wavelength UV. This kills germs with abandon and will happily burn the insides of your eyes if you look directly at it for reasonably short periods. eg 1 minute would be far far far too long.
Long long ago I used this lamp for bulk erasing windowed eproms (some of us are that old :-) ) and more recently it has been used for etch resist exposure or materials testing.
I have used this light reasonably extensively over many years with no obvious harmful effects. As harmful effects are quite easy to acquire (see below) I assume that this means that taking quite basic precautions goes a long way towards reducing the hazard level.
Diagram: Germicidal versus wavelength of interest. Almost

A few years ago I set up some plastic samples under this lamp, placed a cover over the lamp and samples and left it running. Test time was expected to be many weeks. Some time during the "run" I went to China on business. The UV test results were relevant to what I was doing in China and I asked my wife to report on results to date. I provided detailed & careful written instructions on how to uncover the lamp, how to inspect the samples, how to recover the lamp and, very importantly, how to avoid looking at the light in the process, complete with very clear instructions re the hazards. My wife is a competent and careful science professional (in another field) so I anticipated no problems.
Prescript for the queasy: End result excellent AND they swear that while the UV obviously caused the "arc eye" / "snow blindness", the deeper eye damage was unrelated and the UV damage caused it to be found.
Within a day of checking my test samples my wife's eyes became itchy and sore. After a few days she went to the Doctor who confirmed the obvious. She ended up needing both eyes bandaged due to the severity of soreness and burning. Due to the apparent severity she visited the local hospital eye clinic. The routinely interested examiner suddenly leaped up and ran from the room to get a second opinion. In one eye only she had partial retinal pulling causing a subsurface void near the optic nerve.which would have lead to retinal tearing and separation if left unrepaired. This was subsequently repaired by an epi-retinal peel by a suitably skilled man using very very very small sharp things and lots of experience. (Cut hole in eye ...). It subsequently developed a cataract which was removed with a YAG LASER - shine VERY bright focused light into eye ...).
As one does, I did lots of related reading. The professionals are without exception adamant that the retinal problem was unrelated to the UV. They say macular degeneration of this sort happens with age and that the UV event was a fortunate means of showing them that this was happening. My reading showed that in the very very very large percentage of cases (probably 99.99%+) experience is as they report. UV exposure, even very severe and with short wavelength, does NOT lead to premanent damage or to retinal damage of any sort. However, it was also apparent that in extremely extreme cases (eg welding without a mask long term) then retinal damage almost certainly can occur. This is so rare as to be hotly contested by all experts. I'm also aware that if lensing did cause the arc-eye effect (see below) then the focusing MAY have resulted in a focused retinal spot - but the experts all say NO.
WHY DID IT HAPPEN: Uncertain. She is certain that she followed my instructions correctly and there is every reason to think that she did. But, my wife wears glasses for close vision (or did before her eye sight was corrected as a result of the above processes). I theorise that the very short wavelength UV was refracted substantially differently by the lenses and as she looked across and not at the light, the UV was bent into her eye.
(2) Nichia carried out tests on some lowish power (150 mW in max) white "phosphor" LEDs. In the blue region the output was high enough to make them of potential regulatory interest. I'd guesstimate that you could stare at one of these all day long from 100mm and only get bored.
BUT given this result, an LED designed to operate at about 400 nM at about 60 mW input can be expected to output substantially more "somewhat blue" light than my sample and so would technically at least be of potential interest.
BUT the above example with short wavelength UV and the expert opinion re the lack of permanent effect at even high doses suggests that you are unlikely to have any problems if very basic and simple precautions are taken.
Best Answer
The developer is simply a dilute alkali, I use 12g of NaOH in a litre of water. It's quite safe but don't get it in your eyes and wash it off if you get it on the skin. Ferric chloride is quite safe, just wash it off if it gets on the skin. I always wear rubber gloves, both for protection and so that I can use hot etchant with manual agitation (I put the etchant and board in a small container in an old washing-up bowl with about 1" of just boiled water in it).
I've been making my own PCBs at home for about 40 years, using ferric chloride mostly. The only accident I've had that could have been serious was when I was walking across the room with an open bottle of conc. HCl in my hand, tripped, and a little splashed on my face next to an eye. I thought it might have got in the eye, but the fumes were bad enough. I immediately put my face under a tap and flushed the eye out for several minutes. It was sore for a few hours, but there was no damage.