My surgeon provided a compression vest to wear post-op for 4 weeks to help keep bandages in place initially, limit swelling, and provide an extra layer of protection after the bandages came off. As soon as I felt up for it post-op, I went to a local outlet mall and picked up a bunch of Under Armor compression shirts. The vest really started to bother me around the end of my second week, so I called and got permission to take it off early since I wasn't swelling.
I'd say any type of athletic compression shirt is fine. You can probably pick up some decent ones at Target or Walmart. Just don't try to get them at the beginning of any kind of sports season if you're going that route. Both of the stores I initially went to were cleaned out.