He's adorable! I see a lot of TB in him. Whether he's Warmblood or Appendix, I don't know. But he's handsome.
I don't see an "underweight" horse, like stated before, he's pretty under-muscled. A good workout schedule will help with that!
Good quality hay, a nice pasture to graze on and a combination of grain, corn oil and maybe some beet pulp could do the trick for getting weight on and keeping it on him while he's being worked and building up that muscle.
It's very hard to tell someone how to fit a saddle over the internet. I think the best thing you could do is get a saddle-fitter out to take a look at him and help you out. It'd be so much easier and they'll be able to walk you step by step for what you need to look for and how to properly saddle him up to make him comfortable while riding.
"The greatest pleasure of a dog is that you may make a fool of yourself with
him and not only will he not scold you, but he will make a fool of himself too."