Congrats on following through and pursuing a goal!
I'm just finishing up my BMOQ at St Jean and there are few "older" women on the course between 31 and 42, (they would kill me if I called them older, but anyway) the biggest thing I think they have said they needed to work on was cardio. You're running around quite a lot and the last thing you want is to fall off the back of the platoon during runs. There's a fair amount of running about and swimming in other portions of the course as well, so having a good solid cardio base is a very, VERY good idea. Set yourself up on a good interval training plan for cardio and you'll be surprised how quickly you can build up endurance.
As for the strength training, core and upper body is important but so long as you can meet the standards you will be fine. That being said, for every extra push up, sit up, chin up, burpee ect that you can do the easier the course is.
You may want someone at your local gym to "spot" your push ups so you can be assured you're doing them correctly. I can't stress this enough...SOME of the PSP staff are notorious for being extremely picky with their push ups. As an example, my week 8 PT test. My platoon staff counted 42 perfect pushups (I counted 47) but the PSP staff counted 19!! As a former competitive athlete who knows how to do a freakin' push up or two I was not impressed. Anyway, download the CF fitness guide and take a look at that for technique.
Strength training does take time and commitment and lots of repetition. When you have a spare moment, pump out as many push ups or situps as you can, rest for a few minutes and try it again. Do this a few times through out the day. Keep track of what you're doing in a log so you can actually measure your improvement.
Your ability to gain muscle mass in your thirties is more difficult, but if you watch you diet, hydrate and get yourself on a good routine, you will succeed. We had a young woman on our course who couldn't do more than 2 push ups and thanks to our staff and her dedication is well past 25. In fact there's very few women on our platoon whom are not able to reach the men's standards thanks largely to their effort before they came on course.
Being fit is also important for you to avoid injuries as well. I can't tell you how many people I've seen taken off platoon for injuries. Some were unavoidable but many were just due to a drastic change in someone's required output in a given day that they were simply not ready for.
Keep at it and DO NOT slack off on your pre BMOQ fitness schedule. Go fit and be as prepared as you can and you'll be laughing...and crying...but mostly laughing!
All the best to you and welcome to the family!