Drums always first ... use a loop or a drum machine ... gotta get the meter straight. Loops are easier if you're using Garage Band or Logic or something similar, because then you can lock the tempo and the measures, which makes it much easier to edit, set delay times, etc.
Typically, I'll start with a simple drum loop (it's better than a click) for way more measures than the tune will ever be, then lay down some scratch rhythm guitar, then bass, keys, redo the rhythm if I think I need to and then do the lead and vocals last. Then I'll sit down at the drums and put a natural drum part on there. I will do a scratch vocal early on if it's a complicated tune.
You have to get used to how your own voice actually sounds, then usually, it's just a simple EQ to get it sounding good. I like to add some high end to my vocal, with a little bump in the low mids. Studio mics are nice, but really, you should be able to get a good vocal sound with a 57 or a 58. You don't need to spend a ton of money on a mic for demos, that's for sure ... I have a cheapo MXL "studio" condensor and a pop filter for it, and that comes out quite well. I did splurge a little and buy a Rode XY stereo mic to record the acoustic guitar with, and it sounds good.
Things like delays, reverbs, etc., they just mask the sound of your voice ... get comfortable with your voice first, and I think you'll find that less is way more when it comes to effects in a studio recording. Maybe a little room ambience for the voice, that's it. Compression is a good thing to even it out in the mix, but it shouldn't change the character or nature of your voice, just make it work in the mix.