I say this a lot when people ask this question, and I asked it when I got my first one, but you need to test this for yourself. Your fit may not be the same as mine. Get your scope and your rifle, place it on top using coins, popsicle sticks, or something else you can measure between the rail and the scope. I used stacks of printer paper last time. Measure that and add half your tube diameter and you have it the height rings you want.
For years, I worried about keeping my scopes as low as possible. The first time I ever actually used higher rings, I realized I have been missing out for years. The comfort level of going with higher rings has made shooting much more fun. The last rings I had in my Impact were 1.5” tall with 20MOA. I also had an adjustable cheek piece, to make it perfect.
As far as whether adjustable rings are needed to get to 100, it depends on your scope and the distance at which you zero. The scope I put on it last rifle, zeroed at 50, low mount, no MOA adjustment, could not get to 100 yards with the turrets alone. I had to use the reticle for the remaining. Some scopes, especially tactical scopes nowadays, have tons of elevation travel, but target scopes often don’t have as much. 34mm scopes usually have more as well. I would suggest to get adjustable rings or a mount with built in adjustment, so you have no worries. It only helps.