Hey there. I just recently got a MIDI keyboard as well. This is regarding Reaper, I don't use Ableton or anything else:
I would recommend starting with one of the most popular VSTi Synths, Synth1. KVR: Ichiro Toda Synth1 - Virtual Instrument
It happens to be free, also!
Once you have that downloaded, unzip the contents into a folder where you store your VST plugins, effects, etc. I assume you have one already, and that Reaper knows where to look.
Once there, just open up Reaper and it will find the new VST instrument.
EDIT: If you haven't already, go to Options -> Preferences and select MIDI devices. You'll have to right-click and select "Enable" on your KeyRig to be able to use it to play sounds.
One thing about Reaper is that it does not discriminate between Audio and MIDI tracks. So, just make a new track, and instead of selecting the input as Audio, select your MIDI device (it might show up as USB audio device, etc) and select "All Channels" as your input.
Now if you press keys on your keyboard, you should see a small red meter at the right of the track meter in the mixer. That's the level (or velocity) of the incoming MIDI.
Now open up the FX on the new track, and select your synth. It makes it easier if you select "VSTi" on the left, so it displays only VST instruments.
Now your synth should be loaded and you should be able to make weird sounds
For recording, just record as you would an audio track and play your keyboard. After recording, it helps to double-click the newly recorded track and select all the notes and quantize them to the grid.
Feel free to PM me for any more help