Commercially there are two main soldering methods - reflow and wave. "Manual" soldering may still be used to add selected mechanically complex or large parts but this would be rare. "Manual" soldering could include the use of "robots" for the excessively keen.
Wave soldering involves literally passing a wave of molten solder along a carefully preheated board. The board temperature, heating and cooling profiles (non linear), solder temperature, wave shape (even), time in solder, flow rate, board rate and more are all important factors that affect results. Pad shapes and component orientations matter and shadowing of parts by other parts needs to be worked around. All aspects of board design, layout, placement, pad shapes and sizes, heat-sinking and more needs to be carefully considered to get good results. Where used with SMD components they will need to be retained in position - either with purpose applied adhesive instant set adhesive or advanced magic.
Clearly, wave soldering is an aggressive and demanding process - why use it?
It's used because it is the best and cheapest method when it can be done and the only practical method in some cases. Where through hole components are used wave soldering is usually the method of choice.
So - Reflow soldering is less demanding on pad shape, shadowing, board orientation, temperature profiles (still very important) and more. For surface mount components it is often a very good choice - solder and flux mix are preapplied with a stencil or other automated process, components are placed in position and are often adequately retained by the solder paste. Adhesive may be used in demanding cases. Use with through hole parts is problematic or worse - usally reflow will not be the method of choice for through hole parts.
Where it can be used reflow soldering is used in preference to wave. It is more amenable to small scale manufacture, and generally easier with SMD parts.
Complex and/or high density boards may use a mix of reflow and wave soldering with leaded parts being mounted on one side of the PCB only (call this side A) so they can be wave soldered on side B. Prior to through hole part insertion components can be reflow soldered on side A amidst where TH parts are going to be inserted. Additional SMD parts can then be added to side B to be wave soldered along with the TH parts. Those keen on high-wire acts can try complex mixes with different melting point solders, allowing reflow on side B before or after wave soldering, but that would be very uncommon.
FWIW manual soldering, while slow and expensive, is the least demanding of most factors as it usually also utilises biological computing power to control relatively crude soldering instruments in extremely flexible manners. However, precision of component heating and temperature profiles are poor comparatively.
Some modern components (eg Nichia SMD LEDs with silicone rubber lenses) MUST be reflow soldered (according to the data sheet) and MUST NOT be hand soldered or wave soldered.
C: definitely the assembly shop, if you have the wallet for it. That's for you to decide. Ask some quotes, and decide if doing it yourself is worth the effort. Since this is a hobby project you may think your time is free, but then it has to stay fun as well, hasn't it?
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Just got this in a mailing from DesignSpark: fundraising may get you started to have it done by a shop. Erik raised 313 218 dollar for a 5 000 dollar target.
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Alternatively, B: Again, get a quote for a stencil. Yet, even applying the solder paste manually will take less time than hand soldering, which I would not recommend: the resistors and capacitors are not much of a problem, but the ICs may take quite some time if you want to do it proper, i.e. all pins soldered and no short-circuits.
Not A: it takes too long and it's messy. I would only do it myself if I could use the oven.
Remember that Jobs and the Woz also hand-assembled their first batch of Apple computers :-)
Best Answer
There is no generic answer, it all depends on the components involved, let me add a few things to watch out for, and collect for the convenience a few more from the comments.
First of all, read the datasheets of all involved components, what they say about reflow in general and a second reflow possibly.
A lot of things will not be specified in the datasheets though and need to be tested, things to watch out for:
thermal stress during heating (while the part is still held by solid solder) might be too much, especially for MEMS parts and maybe crystals too.
Parts might be held in place by the solder, so watch out for upside down. Also the glue used for holding upside down parts may not be designed for a second heating.
It doesn't seem to make much sense for a manufacturer to specify exactly if a second reflow is possible. In my experience it usually doesn't hurt much, especially if you keep the temperature profile exact.
In the datasheet watch out for any preconditions you might have violated, e.g. if it states the storage temperature prior to reflowing should not exceed 85°C then this might raise an eyebrow about why and if reflowing the first time should maybe count as being store above that temperature.