As if you need more advice! But here goes. The gelding I would opt for since your daughter wants to show and (it been my experience - 8 yrs now) that studs tend to nip more than others. IN fact the only bad habit my stallion has was nipping other people. We gelded him at 7 yr old so grandkids could show him.
If he gets lots of attention from you guys, then he'll more than likely decide you're part of his herd and won't need a companion. But if your time is limited a companion helps them settle and keeps them from being so prone to ulcers. However, you may find that you have to take the "companion" along to your shows too if they get too attached.
We finally brought in pea gravel for our drylots because hubby got so "upset" about all the mud around the barn. He's a neat freak and not a "country boy". We were fortunate that a retired farmer built the barn and had it up on an area that would drain away naturally so a load of gravel fixed all our problems.