Looking for CPU-friendly hosting

[ncjbhd]

I've been on cheapo shared hosting for the past few years, but as my site grows it's getting to the point where that's no longer an option. Specifically, the bandwidth and disk space are fine, but the database has grown to millions of rows; I did a cpanel database backup yesterday and it was sufficient load for the host to lock down the database.

My traffic is usually pretty consistent and the database complexity is irreducible without sacrificing functionality, so what I'm looking for is moreso a stable guaranteed level of resources that won't result in the host shutting down the site when usage spikes, with the ability to easily add capacity when necessary. I've gotten wind that a VPS may be the way to go, but it seems that there's more focus on segmentation of RAM than CPU with those solutions so I'm not sure if it'll mean the same CPU problems again anyway. I'd like to keep costs under $40/mo, preferably around $20-$30 (I'm a college-level kid) if feasible. Any guidance is greatly appreciated.