General
Terry can generally play on any stage pretty well. However it's important to understand how each stage interacts with Terry's and your opponent's tools.
Picking/banning stages are thus very dependent on MU and player preference. Ban your opponent's best stages and play on their worst.
Stage Size
Bigger stages give both players more space to maneuver and avoid each other. If your opponent has a very strong projectile or buff/charge option, you might want to avoid bigger stages.
On the other hand, you'll be less likely to be sent off stage if you get hit while holding center, so you don't have to avoid edge guards or ledge traps as often.
If the opponent lacks a long/midrange pressure tool, Terry can utilize PW and CS and his other burst options to control the midrange.
Platforms
Due to Terry's jump height he can only reach the lower platforms of the following legal stages from a full hop:
Small Battlefield
Battlefield
Lylat Cruise
Pokemon Stadium (PS) 1&2
PS2 requires you to jump straight up or hold in the opposite direction while rising.
Northern Cave
All other platform require an IDJ or a double jump in general.
This makes Terry not really have as much platform extensions as other characters, but Terry can shark under platforms pretty well.
Platforms also offer landing mix ups, especially when combined with his b-reverse specials.
Getting off platforms can be a bit trickier: Terry has a whole 10 additional frames when dropping through platforms to compensate for his super special inputs. Thus he can only really run or jump off a platform to leave it.
Platforms can cover your opponent from your aerial approaches, intercepting Aerials and TK PD.
They also provide an additional option for escaping ledge traps, especially when they go over the ledge.
Blastzones
Terry has reliable options to kill both off the top and off the sides.
Although most of his launchers send horizontally, a lower Ceiling will make it much easier for cRT to kill, especially in the air/on a platform. It also benefits up smash and PG.
On the other hand, having large blastzones can help Terry survive even longer to be more threatening with his super specials in GO mode.
Slopes
Slopes can make the opponent low profile your jab and forward tilt, as well as some conversions into BK/CS. This can make it harder to ledge trap people. It can also make it easier or harder to two frame Terry, depending on the MU. Grounded PW will travel along the slope.
Overall Terry is hurt by slopes more than he benefits from them.
Walls
Terry does not have a wall jump to aid his recovery. However, a wall will prevent an opponent from drifting under the stage to catch Terry's end lag on his specials.
Walls can also be used to tech spikes when your lack of auto snap gets caught.
Terry's spikes will send the opponent diagonally so they cannot tech themselves (unless the Terry was recovering).