I'd suggest these in the listed categories.
BOSS XSV/Infamous Bolt kit.
Lurker takes more time to set up correctly, but gains are greater from it.
Boss is a drop-in product that still does an uber phenomenal job. Saying it's in second place of roughly 25-30 other aftermarket bolts is seriously saying something.
Empire Redline (If you want to get fancy)
Virtue Redefined (BEST LED board. I can guarantee that.)
I'd say Critical, but they're also kind of the only ones who make an aftermarket trigger. If you ever uprgade your trigger, though, consider buying Element Paintball's Pro Threaded Trigger pin. No punch and hammer and accidentally ****ing up your anodize.
Function makes one of my favorites along with Hybrid and the Empire Nano albeit rare is one of the best options to this day.
Nummech makes the contoured Snatch Grip and Foregrip Extender for the Mini/Axe, which on the mini really does make it feel much more substantial and easy to handle when moving laterally. I'd definitely highly suggest the foregrip extender for that matter. Snatch is also a super nice and welcome upgrade, but not mandatory or won't really change your playing comfort/style at all. Just makes it easier to tote around off-game.
As far as barrels, considering you're on a budget, the Lurker .684 Eigenbarrel is your best bet. I'd also get the .678 one as well for the days with smaller paint or cheaper paint.
If you start to look for another gun, refer to the other thread you posted.