Your PAYE payment is your monthly payment for PAYE-eligible loans. You make just one payment (assuming all your loans are with one lender). That payment is distributed proportionately over all your loans (so you're paying off an equal percent of each loan, not an equal dollar amount). In theory, if you could stay on PAYE forever and there was no loan forgiveness, all those loans would then get paid off at the same time.
When your IBR/PAYE application is approved, you get a letter stating what your monthly payment is, and how much of that monthly payment is applied to each loan.
If you can afford it, there's no reason you can't do PAYE and pay off the Perkins loans ASAP. But the Perkins loans are at a better rate--I'd pay the minimum there and apply additional payments to the 7.9% loan instead (you can specify extra payments to go towards a specific loan--if you don't then the lender distributes it amount all your loans). Unless you're counting on loan forgiveness (a bad idea in my opinion), then it doesn't make sense to pay off your lowest rate loans first. Unless you just want the peace of mind of having paid off a loan (which actually is pretty important, and $2500 isn't that much)
If you're really set on loan forgiveness/PSLF (it's possible they'll still be around...), then you could always consolidate your Perkins loans (assuming they're eligible for consolidation into the direct loan program) with your smallest and lowest interest rate loan (such as a $5,000 stafford, subsidized or unsubsidized--doesn't matter, as a subsidized loan will stay subsidized when consolidated)--that way you can keep a relatively low interest rate whilst brining those loans into the direct loan program. But if I'm not mistaken, Perkins loans are actually owed to your undergraduate school, aren't they? So I'm not sure if you can actually consolidate those into the Direct Loan program.
There's no benefit to consolidating other than:
1) Brining FFELP loans into the Direct Loan program (so that they can be eligible for PAYE, PSLF)
2) To get all your loans with one lender (though I think submitting paperwork for PSLF eligible payments does this because FedLoan is the only servicer that tracks that, as far as I know)
3) If you feel more comfortable seeing just one loan rather than ~20.
The drawbacks are your interest rate gets rounded up (so you'll owe more no matter what), and if your loans are at different rates, you lose the ability to pay off higher-interest rate loans first. In theory if you have the money, you should make the minimum PAYE monthly payment, your Perkins payment, and apply anything additional should specifically go to one of your 7.9% rate GradPlus loans. If that additional payment covers more than the accumulating interest on that particular loan, then you will pay down the principle on that loan and save yourself money. It's like investing with a 8% rate of return. Not too bad. (In theory, if you can't pay off more than the interest that accumulates each month, you may actually be better off paying down a smaller loan, since it collects less interest and thus there's less of a "interest hill" to overcome before chipping away at the principle. But this assumes that when you become an attending you can pay down the high-rate loans quickly--otherwise you'd have been better paying down the interest on those GradPlus loans because they'll capitalize at the end of IBR/PAYE)
One of the nice things about PAYE/IBR is as long as you reapply on time, your loans won't capitalize after the initial capitalization (when you start repayment). That really saves you a lot of money. People that borrow $300,000 in medical school probably accrue ~$40-50,000 in interest while in medical school, and at least that much in a 3-4 year residency. But that ~$50K accumulated in residency is basically at a 0% interest rate until you leave IBR. Unfortunately you still have to pay off that accumulated interest before you can chip away at the principle, which is why if you can you should apply all additional payments towards just one loan.
