That's a tricky one.
I've had tenants that were there for a few years get upset when I raised the rent $15 / month.
I think your best bet is to give them proper notice of the rent increase, but plan on them leaving. If they want to stay and pay market rent, so much the better.
Typically some people will leave right away when a building changes hands. It happened to me, even after I met with the tenants and said nothing would change. They get skittish for some reason; perhaps they were thinking of leaving for a while, and the property changing hands was the final motivation. Who knows?
Make sure that as people leave, and you have a chance to get in the units, that things are on par with the market. If you're units are out-dated, have poor appliances, older carpets, or whatever, and places going for market rents are updated; then you make the improvements to warrant the rents. If you avoid doing that, you will have trouble finding renters.
I am not sure how to proceed with the Section 8 person; as I have no experience in that regard. Perhaps someone else will get you an answer to that here.