If you're only smoking now and then and don't want to invest in a lot of pipes maybe look at a meer? You can smoke meers back to back, they don't influence the flavor of the tobacco, and IMHO..... they look awesome once you've got a few hundred bowls through them. I am not a lover of cobs either but they are a good price point pipe. You can also look at clay pipes, Falcons, or estate pipes to keep the prices down. Falcons are nice cause you can get a new bowl for pretty cheap and use the same stem for them all. As far as your original question of if the shape matters..... to a point yes..... but that doesn't mean a single pipe won't let you enjoy good flavor. You just have to be a bit pickier about the shape you choose. I smoke mostly small cutty/dublin style pipes and that works for me as I mainly smoke VaPers and straight virginia flakes but I will reach for a larger bowl for an aro. A size 3 billiard, bulldog, or something along those lines will work well for almost any type of tobacco. Not to big, not to small, just a nice middle of the road average pipe size will work for you.
Do you smoke cigarettes? That will deaden the taste of the tobacco a bit. Maybe switch up what you're drinking when you smoke? Some guys swear by black coffee, others tea, for me I enjoy my VaPers with a Dr.Pepper. What you're drinking at the time will also affect the level of flavor and different mouths work different ways. What works for some might not hold true for you. Take your time, enjoy, and experiment a little..... after all, pipe smokers are know for their deep thoughts and inquisitive minds. Good luck and good puffing.