There's a bit of a wall of text incoming here; there's a lot that can be done with a Stryfe. The Stryfe is one of the, if not the, blasters with the most available aftermarket support.
You have a blue Stryfe, which in addition to being the IMHO best-looking Stryfes, came with a dart lock. This lock is intended to lock the trigger when the magazine is empty but can also lock up the trigger while firing rapidly. Removing that lock is the very first thing that I'd recommend doing, if it's not already gone. It's an orange piece of plastic inside of the blaster that sits above the magazine. You can reach in with a screwdriver through the jam door and pop it off.
If you open the blaster, you can remove the magwell lock (prevents the trigger being pulled without a magazine; adds unwanted friction) and perhaps the rev lock (prevents the trigger from being pulled without the rev trigger being pulled first; some people prefer to leave this one in).
After that, I'd recommend a rewire. This requires soldering. (Bodging it without soldering may be tempting but doesn't end well.) 16 or 18 AWG is good; 14 would be overkill and hard to fit into the blaster. You can omit the electronic locks and (puny) overcurrent protection circuit when you rewire - the wire can go straight from your batteries to the rev switch to the motors and back to the batteries.
Replacing the rev switch is a very good idea for reliability. There's plenty of room for an omron v-series switch inside the grip if you cut away some of the existing webbing. To mount the switch, you can glue in place a plastic block with holes for 4-40 machine screws to mount the switch, 3d print one of these, or just hotglue the switch in after soldering.
For batteries, most people would recommend a LiPo pack. If you clean out the battery tray (being careful not to leave any sharp edges) and use a Stryfe extended battery tray cover (there's many designs available to print for yourself or buy on an aftermarket nerf parts store) there should be plenty of room for a pack. Other options include running NiMH rechargeable consumer cells in the stock battery tray for a very mile power upgrade. Beware of AA-sized lithium-ion loose cells - they conveniently fit in a stock tray but are both a fire hazard and a reliability hazard as they can cause battery holder springs to detemper.
If you'd like to take this project further, you can get drop-in replacement upgrade motors, replacement flywheels, and printed flywheel cages with tighter spacing that result in a tighter grip on the dart. (In IMO that order of priority.) Beware that "180" sized motors require cutting the shell to make them fit as they are longer than the normal "130" sized motors; you can buy or print extended motor covers if you go the 180 route.
If you'd like to take the project even further - this is possible, but probably overkill.
Another "upgrade" that you might want to consider is getting aftermarket magazines. I'm personally fond of Worker's 22-round magazines as they offer a good capacity and reliability while being just small enough that I can fit them into tactical gear.
. . . And I haven't even mentioned cosmetic kits. My point is that there's lots and lots of things that you can do.
Just some add-ons to this in no particular order:
132 size motors will fit if you bend the soldering tabs carefully. The worker half dart kit is quite nice since its compatible with both half and full length darts. Daybreaks / Kepler's are a great option for flywheels (don't get the worker ones imo, I've had some bad experiences with unbalanced wheels from them) If you have a 2s or 3s lipo laying around those are probably the best battery for a higher powered blaster (please do read up on lipo safety)
Lastly find a friend or someone near you that can 3d print parts or get yourself into 3d printing if you're really into the hobby, many sites overcharge for 3d printed components imo.
Wow
Welcome to the Nerf modding community! It can be a bit overwhelming, so feel free to take your time! It's a very rewarding hobby the more you learn!
Can you solder?
Sure can
Then Bob's your bloody uncle
Soldering it for 2s or 3s lipo would be a good start 👍🏻
No matter what your budget is get a decent soldering iron. When I first started modding flywheelers, a basic rewire was a good start, just removing the locks pretty much (this is dead easy on the Stryfe, only three wires + motor bridges!). I think you can put Honeybadger motors in it while keeping the AAs too, but later on you can get into higher performance with a LiPO or NiMH.
Remove the air restriction mechanism and upgrade the spring
Very good recommendation most of the time, but this is a fly wheeler.
