Long story made short:

I'm about to sell my home and I stand to make about $50-60K from the sale.  My original plan was to take $30K and put it on a down payment on another home and take $20-25K and pay off the remainder of my student loans.  However....not knowing anything about capital gains or taxes...exactly what would my tax obligation be to the federal government if I were to do so?  My student loans are friggin' killing me as far as monthly payments go and that my friends, truly sucks.

The laws have changed over the past few years, so you should contact an accountant.  Suck it up and pay for the hour or so...

In my unpaid, unprofessional opinion, you should have no capital gains liability if you  experience a gain while selling/moving from an owner occupied dwelling to a new owner occupied dwelling.

IRS Link

Generally, you can exclude up to a $250k ($500k joint) gain on the sale of a primary residence.

Read Pub. 523 to be sure.

Yes, if it was your primary residence and you owned it for 2 years or more, you should have no cap gains tax.

Section 121 of the Internal Revenue Code (26 USC 121) is what excludes from income the gain on the sale of your primary residence (with conditions and exceptions), so that is the place to start.

http://www.law.cornell.edu/uscode/html/uscode26/usc_sec_26_00000121––––000-.html

It doesn't appear to matter at all whether you "reinvest" the proceeds or how much in a new residence.  From my cursory reading, you could keep the proceeds as cash and it still would be excluded from gain.  And I don't even think you need to report anything about the sale on your return at all, so long as you satisfy the requirements of Section 121 (note that there is a upper limit –– $250k or $500k for married filing jointly, also length of residence in the home requirements, special rules if you sell to a related party or spouse, etc.)

Also check out IRS Publication 523:
http://www.irs.gov/pub/irs-pdf/p523.pdf