The sturdiness of a loom depends in part what it is made out of - if you go to smaller lumber than I strongly, strongly suggest you use a dense hardwood (oak and maple have long been popular). The wood may cost more but in the long run it’s worth it. The wood also needs to be dried thoroughly so it won’t warp. Use quality fasteners. Mortise-and-tenon, dovetail, and biscuit techniques on the joints are also recommended. Your loom will be subjected to significant tension forces, it needs to be strong even on a small scale.
A jack loom has the heddles raised by being pushed up from below, they are jacked up by the mechanism, just as you would jack up a car when changing a tire. Hence the term jack loom. The only threads that move or are acted up on are those attached to the heddles that move up on a peddle stroke.
One advantage to jack looms is they tend to be shorter - all the necessary mechanism is underneath so you don’t have to worry about how much vertical space they take up.
One downside to jack looms is that you need a rigid frame for the heddles, and most use metal heddles. This adds weight. This might be a problem if you have joint or leg issues. When weaving a 40 inch wide piece of cloth on my jack loom at more than 24 ends per inch it can become a work out for prolonged weaving sessions.
A counter-balance loom, without getting too technical, allows for adjustment in the height of the shed (space the shuttle passes through) and the use of counter-weights/pulleys, and other mechanisms to keep the warp aligned properly and under equal tension (on jack looms, the threads that go up are put under higher tension than those that remain still). All threads move with each pedal stroke. Dedicated rug looms are often counter-balance. Think of them as heavy-duty workhorses although you can do delicate and lightweight work on them.
A counter-marche loom means that it doesn’t just lift or drop the active heddles, ALL heddles move on every peddling. This actively pulls the upper and lower parts of the shed apart and is the favored loom for “sticky” warps and very closely set ones. When properly set up, and because they usually use string heddles, they tend to require less physical effort from the weaver.
The downside is that they’re a little tricker to set up (but not that much) and require substantial vertical space for all the required mechanism.
There’s not much difference between counter-balance and counter-marche looms for the beginner. Highly advanced folks can get into screaming matches over the minutiae, as often happens in craft work.
Then you’re probably best off with a counter-marche loom using string heddles. Or a table-top loom although those are much more limited due to their smaller size.
The problem with making your own string heddles is the need for consistency. Can you make dozens or hundred that are identical? Quality control is important. If you need to learn to make your own heddles because sure to allow for the learning curve.