Tbh, it's all up to preference.
Programs
There's no "best", but you have quite a few to choose from. SAI is a popular one, Krita is another one that's getting increasingly popular. You also have Photoshop, Clip Studio Paint, Corel Painter, Manga Studio, Open Canvas etc.
Some of those are free, others cost money. I'd say look around at the various options and see which you come to prefer. Each one are better at some things and worse at other things compared to the others, but none are necessarily hands down "better" than any other.
Sensitivity
Optimally, you want to use a tablet since drawing with a mouse is ... I guess you could but I don't know anyone that would actually recommend it. It just makes it so much harder to control and make accurate lines. It's probably actually better to try sketching with pencil on paper and then use a camera or scanner to get it onto your computer than to use a mouse.
If you insist on trying with a mouse, there's no right or wrong sensitivity, just use whatever feels the most comfortable and change it if it doesn't feel good.
Starting
Why not both? Again, find what works best for you and don't be afraid to look up tutorials and guides on how to draw various things. The important thing is not necessarily what you're drawing so long you frequently practice to improve your technique.