The rules are slightly different if you're selling your car privately.
A good wash, vacuum and clear out will make your car look cared for, but you don't need to go much further than that.
Getting things like the engine bay steam cleaned sounds like a good idea, but people tend to view a spotless car with suspicion, thinking it has something to hide.
Instead, concentrate on more important things, such as digging out the spare key, and finding the service history and MoT certificate.
If the next MoT test is due in a couple of months, get it done - this will impress punters more than a squeaky-clean car.