First of all - considering your level of knowledge and kit thats a great effort - and a really nice song, well done!!
Reaper is a fantastically powerful tool, you wont need more software for a very long time!
Listening to this you need the following kit:-
Decent audio interface
Decent mic for vox/general
Decent preamp (good idea if it takes line level as well as mic)
Decent need not cost the earth!!!!
Read a lot of reviews and check back with us first before buying.
OK in terms of the mix, you need to look at the Reacomp effect. Its a fantastic compressor that used properly will really control those dips in the vocal volume etc Sound on SOund have an online review/guide to it, but read up on how to use compressors first, they are tricky to get your head round, but vital pieces of kit.
You also could learn a bit more about using EQand frequency mixing to be honest.
Another must have is reverbate, which is a good reverb.
Finally did you know that Reaper has a superb inbuilt auto tuner? Look up Reatune in the manual. I'm not saying you need it or not, but its nice to know its there!
Also look downloading other good free vsts - there are huge numbers out there! (my favourite soft filters are free for instance)
If you send me the wavs/mp3s I'll do a Reaper mix for you and send it back. That way you can see what I've done with the effects to make it sound like it does. Hopefully I'll be able to give you some pointers. PM me if you want....
Track 1 on my myspace was recorded in Reaper with a drum kit VSTi called mydrumset which (used to be) free (might not be now).