Parallel transformer outputs

It's a little unclear what exactly you are trying to accomplish. If the point is just to experiment with full wave bridges and see all the signals, then do it at a low voltage like JonnyBoats said. You can probably find a old transformer somewhere that is rated in the range 6-12V AC at 1 Amp or so. That's a good size to put a full wave bridge after, and then you also get a useful DC voltage to do lots of other things with.

As Jonny mentioned, there are also wall wart type transformers that are rated for less power but you can do mostly the same things with. The advantage is that these things are cheap nowadays. You can probably find something in the 3-5 Watt range for $5. Jameco has a broad selection of such things. That's a good place to look around.

If you really want to experiment with a full wave bridge driven by a function generator, then you should power the function generator from a isolation transformer. These are 1:1 transformers meant to take line power in and put line power out, except that the output can float. These will cost a bit more since they are usually intended for 100 W or more. Sometimes they even come in a box with a line cord for the primary of the transformer and a regular output connected to the secondary. You simply plug the cord into a wall outlet, and the thing you want isolated into the outlet on the box.

One gotcha you have to be careful of with these things is that they may not come wired up fully isolated. I bunch of years ago I bought a 500 W "isolation transformer" that was just as I described above. I used it to float a device under test so that I could hook up a grounded scope to it at various places. The first time I touched the scope ground clip to part of the power supply there was nice spark and the fuse blew. It turns out there was actually a deliberate ground wire inside the isolation transformer box connecting the ground from the line cord to the grounds on the output sockets. That's not what I consider "isolation", but someone else apparently does. Once I disconnected the two sides of the transformer and carefully verified there was no conduction path, it worked as intended.

(Note that ready-made power supplies that will fit your requirements are available just about everywhere. These remove safety hazards associated with mains voltage, so they're very much recommended for a beginner.)

Here is a random linear power supply circuit:

Your transformer outputs AC, so you need to 1) rectify it using a diode bridge and 2) bring it down to regulated 5V using a linear regulator. The transformer should be rated for the current you need with some margin.

Output voltage of your transformer should be somewhat larger than desired voltage to take into account linear regulator dropout and diode drop, but not too large because any excess power will have to be dissipated by the regulator as heat.

Diodes should be able to withstand both forward current and reverse voltage (this is essentially guaranteed automatically for power diodes). A 1N4007 (rated for 1A) will likely fit. If not, cheap 5A diodes are available. A diode bridge is more convenient than 4 individual diodes.

The regulator (7805, LM1117-5.0 or any number of other ICs) should also be rated for the current you need. Note that a heatsink might be required.

Choice of capacitors is normally dictated by the linear regulator datasheet. There's normally some minimum value required for stability. The capacitors should be rated for voltages they're under. Note that the voltage is >5V for C1, and it's also pulsing, so make sure you provide a large margin for safety.

Note that you really want a mains switch and a fuse before the transformer (not shown in the circuit). Also note that mains can kill you, so read up on electrical safety before doing anything if you have not done so already.

Everything that is connected to mains is connected in parallel so that full mains voltage and lowest possible source impedance is available for every device.