First you might want to let your host know that there is a problem and you are considering a move. They may move you to a different box with fewer / safer neighbors.
Then look for a better shared host.
VPS does have a sharp learning curve. I've done what you are suggesting. With WHM and Cpanel it still takes a lot of time to keep the server running well. Between all the mail and anti spam systems, ftp, firewall, perl, php, sql etc there is just no way a novice server admin can keep the server running smoothly with quick response times.
I've just moved back to shared hosting after fighting for 2 years to keep a VPS running. I was with vpscolo who were great but the time wasn't worth the advantages. Now i'm with shared at diligenthost, so far the fastest shared host I've ever had. And great service. They did a server to server transfer for me.
If you want to become a server admin get a VPS, but don't put any clients or critical domains there until you have it well under control. I lost a large client by moving them in before the paint had dried.
Good luck.