RAM usage - absolutely minimal. Windward's TNet server uses about 300 MB of RAM. It depends on how you use it though. Every time you upload or download a file, TNet will cache the latest version of it in memory to speed up the retrieval process for the next time. This obviously accumulates memory. Restarting the server clears it, and you can modify the server's source to release the memory on demand too if you like. I'm sure I'll add the functionality to automatically release the file memory after a certain time has passed at some point. And no, you don't need databases. TNet can save/load files for you, and it automatically saves any player data you assign to the player, provided you've specified what save file the player should be using (explained in a tutorial).
If you want a racing game, then you will want the minimum possible latency, implying several servers around the globe. Players would join a lobby and pick a server from the list that they want to play on. Processor usage is going to be minimal on the server side since all it does is echoes packets. Your only true concern is the bandwidth. Racing games generally mean a lot of frequent packets, so the server's IO responsiveness needs to be high. I would suggest having a peer-to-peer gaming functionality either instead of, or in addition to your server-based gameplay. Makes it much easier to have LAN parties and to simply play with your friend(s) in the same room.