left/right noise = your throw is not in a linear pull and the result is you have error tendencies to let the disc slip/push early or grip/pull late.
correct on the 150 class teebird.
as for the leopard, i personally would move away with it once you can really control it and then focus on throwing discs with a more predictable finish. the gazelle, cyclone, and polaris are basically the same speed as the leopard.
as for next driver, you will find out preferences in the meantime. the jls, xl, and teebird are not forgiving discs if you get them flipped over sufficiently. imo, it is a lot easier to consistently throw an eagle, gazelle, cyclone, etc. as they are much more forgiving.
you could honestly move to the valk right now probably, but imo, you should get a feel for what traditional styled discs do. nowadays design uses speed to suppliment stability. older discs were stable/understable by nature.
out of the discs i listed, the XS, XL, teebird, and Valk are the longest and the eagle and jls have "enough" d... however, you will likely want a disc that will fly near max D at a low trajectory. imo, you can feel free to step up whenever you want to discs like the beast, flash, wildcat, orc, etc., but you should have the foundation of the game already there vs. building your foundation upon those discs.