Hey there! I'm also personally influenced by western animation in my work. I use a combination of Paint Tool Sai 2.0 and Photoshop. You can see some of the art I've made with it here:
Paint tool Sai 2.0 has a stabilizer that you can activate, which is helpful for me, although it certainly isn't for everyone. It essentially "corrects" shaky lineart and gives that smooth, digital feeling, which a lot of cartoons have and have had in the past. I like it better than pen tool in Sai and Photoshop, although that can work as well for this. Stabilizer feels more organic since it's a free handing technique, while pen tool is not.
Sometimes the exterior lineart isn't as thick as I wanted it to look, and for that I use Photoshop. Photoshop has a "stroke" feature, which is particularly useful with transparent png images. While it isn't always as precise as I would like, it can have some great results depending on the image.
This is an image that I corrected with Photoshop's stroke. The lineart around the character was something that I wanted to be thicker than the lineart on the interior of the character, but I hadn't made it that way initially. I think the difference is nice, however!