Congrats on stepping into the world of elk hunting!
I applaud your efforts to go with a guid your first time (maybe first couple). The learning curve can be steep and expensive, and if your goal is to provide your son with a memory, a guide will give you a great shot.
Private land DIY (like where you pay and access fee and that's it) is not really a common option. We do have a poster on here who used to have some private land tags available, so he might chime in. But, you need someone to teach you more than you need access.
Your options will really depend on your budget. A guide who has you on public lands with an OTC tag will be cheaper than a private land tag. Both will be cheaper than a high fence operation. Any of those can be a truly fun hunt, depending on what your objectives are.
A drop camp style hunt is a true experience. Ride in on horseback to a preset camp, canvas tents and stoves, campfires, LOTS of stars and rugged scenery. The guide can drop you off (drop camp), or guide you the whole time. I recommend having the guide. You can find these from a couple grand up to $4-5K. With fully guided option, they will generally handle the cooking and stuff too. But you might need a party of 3-4 to make it work. You will work your butt off, and will probably see some elk. You might get a shot at one too. But coming home with all tags filled is definitely the exception, not the norm. Know that going into it, especially in Colorado.
I have a recommendation in southern Colorado or in New Mexico if a backcountry camp is what you want. The New Mexico hunt might be slightly easier, but with a bit higher odds. The CO hunt is epically beautiful and extremely rugged. I am only speaking of the 2 I can recommend, not making general statements about the states.
Another option would be a guide on public lands, but essentially doing day hunts. I have done this with my Dad in Colorado and New Mexico. Success rates are not much different, but its a lot less work. Generally staying in a hotel, camp house, or low camp each night - and driving to different places to spot and stalk. It is a fun way to hunt. It can be a little less physically taxing, but not really easy at all.
Lastly, would be a private land hunt. This will almost universally be your highest success rate, and probably best accommodations. You can find places with full 5* amenities, or places where you stay in a little camp house. But, you aren't fighting the crowds, and the elk can be a little easier to pattern. This gives you the best chance to fill a tag or both, but will usually come at a higher cost. You will still learn a ton about elk hunting with this setup.
I can rec you a guide for CO or NM in any of these categories. I can also point you towards a high fence place in CO (Smaller HF ranch, guaranteed success, but they also have low fence options that are fair chase hunting but have nice facilities) or one in ID (huge bulls, huge ranch, hard hunting, HUGE price tag).
I hope this gets you started thinking.
Don't hesitate to ask 100 questions. Now is the time to learn!