If you don't have one already, I would recommend a pellet gauge. For me it is very valuable to know the head size of the pellets (you can't go by the tin label). For example, I have some old H&N FTTs that shoot great in a couple of guns and measure 4.51. I bought a couple of new tins of FTTs and they measure 4.53. They shoot like crap out of everything but an old RWS48, and the velocity is down about 60 fps compared to other pellets that weigh the same. Knowing that a particular gun prefers smaller head sizes helps keep me from buying a bunch of pellets that won't shoot accurately.
You don't have to go crazy measuring. I just take about 10 or 15 pellets from a new tin and check them out. If most of them are a consistent size, I mark the size on the tin. If they aren't consistent, I use them for indoor practice.
If you don't want to spend $50 on a pellet gauge, you can measure the heads with calipers. It's not quite as accurate (at least the way I do it) but it should give you an idea as far as what head diameter your barrel prefers. Once you find a good pellet, you can measure them and buy more in the same size or try other pellets in the same size.