M.2 is a shape. That's all. If it's a Sata M.2 it's the same thing as a 2.5" plug in Sata SSD. No difference.
If it's NVMe M.2 that's different. They can be and generally are considerably faster, especially in the higher Gb, a 2Tb NVMe has a longer expected lifespan, and generally out-performs a 500Gb/1Tb NVMe.
In large ( game files are tiny, even maps aren't that big, I'm talking about 1000 page legal documents, full game zip transfers etc) file use only. So with games there's relatively no difference between Sata and NVMe, it's only noticeable as a second or 3 in a side by side comparison.
Gen3 NVMe/Sata don't usually get hot enough, even under heavy loads, to require a heatsink as such. They come with a heat exchanger in the form of copper strips built into the sticker, and thats plenty. They actually work better and suffer less wear and tear when warm, so it's a good thing for Gen3 to be open air.
Gen4 (pcie4.0) gets nasty hot, especially when loaded down. So you will want, it's basically a requirement, a heatsink. All the Gen4 come with a heatsink, whether you use that or use the fancy one on the mobo or another heatsink of your choice is upto you, but use one you must.
The Z390 Gaming X has 2x M.2 ports, both accept Gen3 Sata or NVMe, so a Gen4 NVMe is useless, it'll be crippled to Gen3 speeds, too expensive to consider.
So you have Sata or NVMe choice, Gen3. On a budget, I'd say a 2Tb Sata M.2 would be good, it'll do everything you need with extra space, but if you decide you'd prefer NVMe, you'll still be restricted to Gen3, and you'll pay more for a little more usable speed at a little/lot less space.
Crucial Mx500/550/P2 are good, as are WD SN550, Samsung 850/ 960 or better etc. Sabrent and Silicon Power aren't too shabby for uber budget stuff.