The post-surgery compression is snug, although my surgeon put it on me and told me to simply not remove it at all until I came back in for my first post-op visit. It was pretty much like a binder, although not as tight.
The silicone strips I use are 'ScarAway', and I used them sporadically at first, along with some scar cream. Recently I started using them again, wearing them 24 hours (except for a break while showering) and it's making a noticeable difference on my scar healing. So even though it's kind of annoying to wear them for months I'd still recommend some kind of scar strips, it's worked so much better than just the cream/gel.