@Matt Watson - Hi Matt - I've rented to section 8 tenants before. It's a mixed bag, but the guaranteed money is good. When I bought my triplex in Seattle, I opted to keep the existing section 8 tenant because she'd been there for 7 years. Her rent was below market rate so I immediately brought it up to market and let Seattle Housing Authority know of the increase. Sometimes they will balk at the increase and say the tenant cannot afford it, but just push that it is market rate - just because its section 8 does not mean you lower the bar.
In terms of not renewing the section 8 leases, give them plenty of time and a heads up that you're not renewing their lease this year. It'll give them time to find another rental that will take their voucher. I would even offer to be flexible with their move-out date. You can also give them a reason such as "I'm the new owner and I want to renovate all the units starting with yours". Read their lease agreement and see what the language is for terminating their lease - Mine was 90 days notice and not the standard 20 days (if they're MtM). If they have kids in the school system, consider extending their lease as month-to-month and terminating between July-August so they have time to move and set their kids up at another school district.
To reiterate, the key is to make it as easy as possible for the tenants if you want to minimize negative responses. And... document everything including notices you give to your section 8 tenants.
I am a licensed agent in Seattle and I specialize in 2-4 unit rentals. Keep me posted if you have any other questions or if you need help making an offer on that triplex.