@sajha keto
1. "Apply for TPS and just keep it as back up. After getting married you both show up for interview, get h1 for you, h4 for your wife and travel on H visas and do not use TPS AP for travel." Does that mean I should not apply for AP or apply for AP and take it with me as back up so that if H1 stamping is rejected, use AP to come back?
You can apply for AP if you want to keep as a back up, but priority should be coming back on H1 visa, not AP.

2. Would there be any issues in H1 stamping as they should be aware of my TPS? I mean does TPS affects stamping on certain visa type (H1 in my case and H4 in her case)?
As long as you are maintaining the requirement of H1 even after TPS approval, TPS will not affect your other processing. H1 and/or H4 approval will be solely based on your job and your qualification as usual.
3. My H1 starts in October and I am in OPT now. Which one of the following would be better in your view?
a. Applying TPS after H1 starts
b. Apply now in OPT and starting october, H1 will automatically be started

It does not matter. But since Oct is just weeks away, apply in Oct first week since H1 gets started from Oct 1 if you have any doubts.