Yes, Lylat is by far your worst stage as Fox. Smashville is your second worst starter because of the close side blast zones and relatively small stage. Battlefield and Dreamland are Fox's best stages, as he benefits greatly from platforms to extend up air juggles and provide additional places to recover to. Town and City is similar with its low ceiling and platforms, and Duck Hunt is great for us because it has lots of room to run around, a wall to help our recovery and the flora and fauna can help extend our juggles.
Overall, I'd say:
1. Always strike Lylat unless your opponent doesn't like it either. A Fox game should never go to Lylat.
2. Always consider striking Smashville game 1, especially vs Diddy, Sheik, etc. Strike another stage if you personally feel like it's worth it for the MU (e.g, Battlefield vs Cloud, FD vs Villager).
3. On your counterpick, you can pick from T&C, Duck Hunt, Battlefield and Dreamland depending on the MU and if/where you've already won games in the set.
Also, Final Destination is a great Fox stage as well, but doesn't have some of the benefits of the other stages. It's not a bad place to go game 1 (a lot of my game 1's go there) and is a good counterpick, especially against other vertical pressure characters like Cloud and ZSS.