Another definitely wear a lifejacket here. If you haven't swam in cold, moving water with all your clothes on lately I think you'll be surprised how intense it is. I'm a good kayaker and swimmer and I'd never get in a packraft without one (especially in the spring).
I'd recommend one designed for kayaking (NRS, Astral, etc...). Even the cheap ones will cost you $100+, but they work really well. You could probably survive with a walmart special, but it will suck in every way.
Whatever you buy, you need to be able to cinch it down so that when your buddy pulls up on the shoulder straps it stays mostly in place.
Edit to be more actionable: if I couldn't try them on and wanted to keep cost down, I'd buy
this one or
this one. The extra $25 is worth it for a side zip for me, but not necessary. If I wanted to get something nice that I expected to use a lot, I'd get the NRS Ninja recommended above (the low-profile design is nice and is standard for kayakers). If you can find a similar style by a reputable manufacturer on sale, I'd buy that.