It looks like your buggy has a 3660 motor in it. 36 is the diameter in millimeters, and 60 is the length in millimeters. That's your first step.
Motors will generally come in diameters that are compatible from brand to brand. Mounting holes are the same, etc. Like 36mm is a standard 1/10 scale motor. Smaller, lighter RTR RC's will usually use a 50mm can length. But you will find them in various lengths. And the longer they are means a longer stator, and longer magnets, meaning more torque. More torque will allow you to run a bigger pinion usually. Just a bit of info to get you started.
Since yours is a rear mounted motor, the length probably isn't too critical. So check your motor and see if you can get by with a 3665 (5mm longer). That may give you more options, but to be honest, 3660 is probably more than enough for that buggy.
Spektrum motors are decent, but their ESC's lack a lot of features and settings. So a good Hobbywing setup will definitely be an upgrade.
Gather the specs:
Your motor is a 3100 kv, meaning for every volt applied, the motor will spin 3100 rpm.
It will run on 3s, and a fully charged LiPo cell is 4.2v. So 3s (3 cells) is 3 x 4.2v. So fully charged your hitting 12.6v.
So take your kv, and multiply it by your max voltage and you get 39060 rpm. Brushless motors are often ok up to 50-60k rpm or so. Some more, some less. Staying on the lower end will keep the motor running cooler, allowing for bigger pinions, and more SPEED!
With that info in hand, I'd maybe go find you a motor with a bit more kv, or a 3665 can which will allow you to run a bit bigger pinion with ease. Or BOTH
Here's where I would likely go, but I don't know alot about that buggy, and this is just my best guess at what would work pretty good. The 3200kv is what I was looking at here...
https://www.hobbywingdirect.com/col...run-max10-combo-3665sd?variant=40522184228979
Your stock pinion is (I think) a mod .8 - 16 tooth pinion, with a 5mm bore. Robinson Racing makes nice pinions.
https://www.amainhobbies.com/robins...-gear-w-5mm-bore-11t-rrp8711/p454473?v=186534
I would grab a couple bigger than your stock one, if that is indeed 16t, I'd skip 17 and grab an 18t and maybe a 19t or 20t. Maybe it will take bigger? Then you could dial in more speed, if that's what you're after. But bashing around the yard with a 4wd buggy, jumping, etc - torque baby! Use your pinion to dial in that sweet spot where a blip of the throttle leaves a blur, and the buggy is gone!
But the first thing you need is an infrared temp gun. Grab a cheap one off Amazon so you have it on hand before you run it. You want to keep the motor and ESC around 160°F or below. If you slap the 18t on there and it's only hitting 130°, put that 20t on there and retest.
Word to the wise, if you aim for 160°, and you tend to do a lot of high speed passes, back to back, and run it like that, if you start getting some bearing or other drivetrain issues...
If you're testing shows with some high speed passes it hits close to 160° and you typically just bash around the yard and stuff, you are going to be just fine, because it won't be hitting those temps.
And welcome to the greatest RC forum on the planet