Welcome!
Recurve or longbow....? I personally prefer a longbow but have about 15 recurves and two longbows. Mainly I bought all the recurves because I got good deals on them from yard sales and the big online auction site. Never paid over about 75 or 80 bucks for any of them and got some for as little as 5 bucks. My longbows though were both custom made for me personally. One of them is my "go to bow" 99.9% of the time.
Like slasher said, just carry the bow in your hand. My longbow weighs a little more than a pool cue and at 66 inches long there is only 33 inches sticking out to the front when it's held horizontal at my side. Nothing at all if held vertical. I used to fly fish with a 9ft fly rod in thick nasty creeks in PA and never had much of a problem toting that thing around so the bow is a piece of cake. If you are climbing mountains and need your hands free, I could see the need for a takedown model, otherwise not so much. I personally prefer the looks of a two piece (look like a one piece) and there are multiple styles from hinges to sockets, quarter turn fittings and bevel locks. All work. The big benefit of a three piece is you can later order another set of limbs in a different weight or length.
If I were you, I would look for a used one piece recurve bow on line in the 45 to 50 pound range at 28". Keep things under a hundred dollars. And yes, that's not too hard to do with recurves from the 60's and 70's if you don't have your heart set on something collectible like a Bear. Lots of Ben Pearson, Root, Herters, Shakespear, Wing etc options.
Since your draw and your sons draw are both under 28" you will be pulling less weight than what is marked on the bow but learning will come faster with a weight that is zero strain. In just a few weeks, you will be able to pull more weight and will also have had time to try to hook up with other trad shooters in CA or find a trad shoot to go to. Most shoots have vendors selling bows and sure as shooting, you will get a bad case of "new bow-itis". You will find something new, custom and exotic that shoots like a dream and you'll want it BAD.
Since you only spent a pittance on the used recurve you started with, no big deal. Buy the new one, sell the old one or, if you're sentimental like most of us, keep it and use it as a backup or maybe for bow fishing. (Talk about a sport that will turn a bow into a beater!)
Come fall, the 45-50 pound bows will work just fine for deer if you don't move up to something else newer and stronger. Just be honest with yourself about your ability and keep all shots inside your slam dunk shot range and 40 pounds will do the job just fine.