so 240 slots being used that's about 2GB of RAM at least min required for that for SAMP that I'd recommend. CPU depending on your gamemode and well optimized it is you could be using more than one core for all you know or just one core of at least a 3.4GHz core.
TS servers eat up RAM and bandwidth as well and a bit of CPU.
I'd say you need at least a Dual Core CPU but I'd recommend a Quad Core depending on your gamemodes.
With the TS and servers on a linux box I'd suggest 4GB of RAM. 240 players, 80 slots of TS being used I'd get at least 1TB of BW as well.
I wouldn't use a cheap VPS for these services either as if they're on a 100mbits network speed it's shared along other VPS's and likely you will be limited and have major issues.