That's a pretty big question. If you haven't already, you might could
start here first.
I use a Rev Solo II pickup, and sometimes a Planet Wing. I use a Beyer M 88 TG mic, and sometimes an AMT.
If you just started playing double bass, I'd recommend trying to find a teacher. It all starts with your acoustic (unplugged) tone. Part of that involves settling on strings that make you and your bass happy. DB strings cost a lot more than EB strings. I'd also suggest finding a good luthier to make sure your bass is playing and sounding its best.
Then come back here and search a bit. Other popular pickups these days include the Fishman Full Circle, Gage Realist, K&K Bass Max, and the Underwood. I've probably left some out.
Using a mic can be challenging, even moreso if you run it into your amp because you don't have a PA. But the sound is worth it. For mic and mounting ideas,
check this out. Or search this forum for titles of threads that include 'H-clamp'.
Welcome to our wonderful world. You're gonna dig it, but it does take some patience, determination and dedication. But when you hit that low F on DB and can make it growl, it's all worth it.