My agent did these things for me, so I might be slightly inaccurate in what you can and can't do before being invited. I know that you need a HAP number generated, in order to get your health checks done. I believe this might only be possible once you've been invited, but I could be wrong. The police clearance is valid for a period of months (I believe this is 12 months) , and you can do it at any time.
If you've not filled in form80, do so now. It's a pain in the arse, but it's worth just getting it over and done with.