Selecting a put hedge involves several trade offs. It's like home insurance. If you use a select a higher put strike, you pay more for the hedge but you have better protection. If you use an OTM put, you pay less for the insurance but you have a higher deductible (the underlying can lose more before the insurance kicks in).
On an options 101 level, set up a spreadsheet that calculates the cost of the entire position (underlying + put), the upside break even point, the maximum loss point, the amount of the maximum loss and the cost per day of the put. Uses a number of strikes, starting with ATM and lower, adjacent strikes. That will show you the trade off of cost of protection versus amount of protection. Then compare the results of all puts analyzed and look for the one where the risk versus cost is most suitable for you.
If you have a higher level of option experience and access to option analytics, graph each put/underlying combo. If the program offers time slices, you can observe how each combo position performs over various time periods between now and expiration.
I like collars for hedging since they can be structured for little to no cost. Of course, you have to be willing to give up the upside. If the underlying cooperates and rises gradually, you might even get to roll the collar up, locking in gain while giving yourself additional upside profit potential (a debit unless near the upper strike at expiration).
Since you mentioned theta, avoid short term options for hedging unless
(1) you have some magically ability to time price movement well or
(2) you are collaring
...because otherwise, the premium will be like sand in your hands, disappearing faster and faster.