Hi KrisB
You have to get your timing right, as you are in receipt of ESA your best time to apply is just after your ESA hits your bank account.
ESA is paid every two weeks whereas UC is paid monthly.
PIP has no effect on your UC claim, as you are in the support group, you should be placed in the LCWRA group without having to supply a fit note.
You may want to discuss with your local Welfare Rights Organisation:
advicelocal.uk, the best time to apply.
Gary