As far as I'm aware what you have is one of the earliest brushless systems. the 5800 was designed as a mild modified. Have a look at what the lowest turn motor your ESC manual says it will handle, then find a modern motor of that turn, that should help you go fast as cheaply as possible.
To go to LiPo batteries you will need a low Voltage cut-off, without it you will damage the LiPos when the dump. The newest ESCs have this feature built in. So maybe think about a new ESC as well.
I'd been out of the sport for a few years until recently too. I came back racing 12th only because it was the only class I could compete in with old gear, and then only really at club level. I'm only just updating everything now, and finding I pretty much have to do it all at once. Do you realise 12th scale cars don't even have T-bars anymore!?