I see already a lot of great suggestions here but let me throw in my own:
For sustain, yeah compression would be ideal for you. I would actually suggest you to try the Boss CS-3 pedal, which is a compressor sustainer. It's in the budget friendly side of things so I think its a great options. There other compressor I loved like the keeley and many others but I would start and see first if the CS3 solves your sustain issue.
Now reverb will definitely add on to help create those more ambiant sounds. For pedals, I actually stand with
@Ids Schiere. The Hall of Fame is one the most brilliant reverb pedal on the market and it still remains somewhat budget friendly and it has a lot of great feature.
About the amp itself, to be honest, it's a practice amp so it's really not the best for where you are now. Now with the Line6 spider, they have their reputation and I will say that the most recent ones have been better however, for where you are now, if you consider upgrading your hardware, I would actually suggest you to move on from the practice amps and get something more versatile. And in this scenario, I would suggest pedalboards as they really got amazing over the years and I think this is where the future is going. At least, that's what the trends suggest.
So my ultimate recommendation in that department would be the Line6 Helix. Those have been simply amazing and there are different format for any budget. Plus since I know about your awesome sound card, you can plug it in directly and use it as your FX processor for any guitar recording so you could directly use it to record demos or whatnot. And since its an FX processor with a large banks of FX, you bet that there are reverbs and compressor in it (tuner as well) So you could better manage to find your tones! The HX Stomp is a great compact option or you can go for the HX LT!
But yeah those are my suggestions! Good luck!