Three-button suits: My preference is for two-buttons on suits, but three buttons can be fine if you remember a few rules. First, only button the middle button. Second, have your tailor (or perhaps an alterationist) turn the jacket into a 3/2 roll. You could also try to do this yourself, if you feel confident enough to do so.
As for the pants, I took a look at the Banana Republic website to get an idea of how they’re styled. I would probably get them tailored, too. I would probably first make sure they were hemmed up so they have “no break,” then have them tapered to a 7”-8” leg opening (I typically go 7.5”, sometimes 8”, it depends on the pants, fabric, etc.). I’m not sure how the pants look in the back, but you may also consider having the tailor take in the seat as well.
Just looking at how they style their pants, for a skinnier guy they seem to be baggy off the rack. A taper down the leg will look much better. All told, this shouldn’t cost you more than $50 (probably more around $30).
Good luck! If you can, take some before/after shots and hit me back.