When asked 'cockpit checks report complete' I respond Wilco and then call 'checks complete' when they are done. If they are already complete I say 'checks ARE complete', with the emphasis on ARE. I never respond to the initial request 'checks complete' as I believe that there is scope for misunderstanding (am I acknowledging that I will report when checks complete or that I have already done them).
On final approach (some time after ATC say 'do not acknowledge further instructions unless requested') they should say 'check gear, acknowledge' to which any response of 'three greens' or 'gear down' should suffice. You may also get a 'cleared to land, acknowledge' call which is self explanatory.
As others have said, you should get a 'begin descent now for a three degree glidepath'. If you don't get this then don't descend. If ATC have forgotten they will have to feed you in again. For a PAR you should get the following glidepath info, on glidepath, slightly below glidepath, below glidepath, well below glidepath-acknowledge (and the opposite for above glidepath). The final call requires you to say 'acknowledge' or something similar and is just a safety check.
For SRA, as has been mentioned, you are told your range and target height and it is up to you to make it.
Finally, without teaching you to suck eggs (as I don't know your experience) but if you don't know the differences between the two then get someone who does, to fly them with you and teach you how they work (I assume you are instrument rated?). There are some technical differences that haven't been mentioned here, such as PAR being a precision approach and having a DH whereas SRA is non-precision and has a MDH.
All these comments refer to military approach. I can't remember having flown a civvy PAR (or SRA for that matter) and the terminology at civilian fields is different. Be aware that if you are at a military field you will most likely be set up to approach on QFE unless you ask otherwise. At a civvy field you should be on QNH unless you are asked otherwise. You really don't want to get this wrong.
I hope this helps.