Actually, in my experience the first bottleneck I ran into when running a webserver on a VPS was bandwidth. Either saturating the actual bandwidth, or running out of allowed open sockets/connections on the VPS. The former you can't do much about unless your host allows you to buy more bandwidth, but the latter at least can usually be tweaked by the hosting company. After bandwidth, memory was the next limit I hit, mostly from running SpamAssassin at the same time as MySQL, Apache, etc. I resolved that by upgrading to the next level plan with more memory available.
If you haven't already selected a hosting company, I can recommend Tektonic. The prices can't be beat and if you get the middle or higher level plans they have a decent amount of RAM and CPU. Bandwidth is not metered, you're capped by actual capacity instead so if you find yourself short on bandwidth you'll probably have to pay for additional capacity, as with any host.