As far as I know if you're taking out new loans you're not eligible for PAYE, but maybe the people who were eligible for PAYE and take out new loans are. I had one loan I borrowed before the cutoff (Oct 2008 or some other random/arbitrary date), so I unfortunately wasn't eligible.
All the other repayment plans have 25-year forgiveness. As of right now forgiveness via IBR/PAYE/REPAYE is treated as taxable income, so you actually take a big hit and would need to do the math to see if it really makes sense to make payments for 20-25 years, while allowing your loan balance to balloon, and then pay ~30% taxes on a loan balance far above $400k (unless you make payments large enough to cover the interest).
PSLF is certainly a nice option, because if you work for a non-profit for 10 years (most, but not all, residencies qualify) and are making your PSLF-eligible payments (like IBR/PAYE/REPAYE) then your loans are forgiven tax-free. But most of us feel that program will be changed quite a bit, if not cancelled.
In the end, you should count on repaying back every dime your borrow. Don't count on or expect forgiveness because we don't know what will happen to these programs in the future, and if they do go away you don't want to be repaying your loans after 30 years.
If you're not comfortable paying off that much debt on a normal payment plan (ie, no forgiveness), then I'd argue you shouldn't borrow that much in the first place.
I was in similar shoes as you and I did the math, looking at my expected salary (PM&R) and how much debt I'd finish residency with. My take home pay will be crap for quite a while, but it was worth it to me--job I enjoy and find meaningful, great job stability, and I really don't need/want a BMW or McMansion anyway. But most med students and residents I run into want to be rolling in the dough for all their hard work (and it's a lot of hard work).
Still, do whatever you can to minimize how much you borrow--get a roommate, cook your meals at home, drive a cheap and reliable beater (ie, Honda Civic), consider biking/walking to school the first two years, don't drink/eat out every couple days, etc. etc. Medical schools give you way too much money for living expenses--you really don't need that much. Trust me when I say when you actually start repaying your loans, you will have wished you had borrowed less.
