What can this VPS handle?

VPS
Shared CPU XEON 4-core 2.33Ghz
1GB RAM
(30GB HDD)
1Gbps datacenter
Ubuntu Server, there will be no problem changing to some other Linux OS like Debian.

How much GMod slots and TF2 slots can this machine approximately handle please?

You mean at the same time? Or one or the other?

1 GB of ram won’t hold that much.

In all I would say one 32 slot server to two 16 slot servers.

how much tf2 slots
and how much gmod slots
not at the same time
more like 2 different machines

10-12 for Garry’s Mod (if you want it to play smooth at capacity)

No idea about TF2

Your RAM is a little low to be hosting servers.

Up the RAM to have more stability.