Let's get two things cleared up immediately; there's undeniable health benefits but also potential health hazards associated with standing for extended periods of time. Just do not listen to epidemiological studies. Ever. You’ll insane nonsense like “standing up at work doubles your risk for heart attacks” and “sitting down causes increased risk of cancer”. It truly amazes me how anyone can take “studies” like these seriously. Epidemiological studies are numerology at best, but I will go more in depth on that topic in another post.
So let’s go with actual science. You will burn slightly more calories, but nowhere near the amounts touted around the net. Blood sugar spikes will be reduced if you stand after eating.   Standing will strengthen your back, leg, core and lower back musculature which is a common problem for many whose occupation involves a lot of sitting.   It will strengthen the entire kinetic chain starting with you feet and ending with your upper back and neck. 
I noticed the benefits on my back musculature almost immediately but the real “killer feature” for me was the massively increased focus and energy levels. Instead of zoning out or feeling sleepy in the afternoon I’d be alert from start to finish.  This is a natural reaction, when you’re on your feet your body will keep your sympathetic nervous system active in case you need to hunt for food or run from danger.  If you’re sitting down it’s much more likely to activate your parasympathetic nervous system which kicks in when you’re digesting food, basically it wants you to get tired so you won’t use up as much energy. Rest and recover. 
Be warned, your feet will hurt. I went from sitting down roughly 16 hours a day to standing for 13, I don’t sit down at all since it’s just my inner weakness trying to manifest. Never let it. You can rotate between standing and sitting if you lack character, it’s better than only sitting down but watch it. If your feet, particularly your heel, starts going numb and then hurting deep inside you’re likely forming heel spurs. I stood on the floor and then an entirely too hard gym mat, ended up almost ruining my right foot. Buying a 2cm thick gel-mat and doubling it up cured the issue entirely. You do NOT need to buy those overpriced standing desk mats.
It does not matter which desk you buy. Just get one appropriate for your length. Experiment with postures, the recommended one where your monitor is on a stand raised to eye level with your arms going in a 90 degree angle did not work at all for me. I raised the desk until the top of the monitor was at eye level but without a stand, resulting in my elbows and arms resting on the desk. Very comfy. But that might not work for you. Constantly shift your weight from leg to leg so you don’t develop muscle imbalances.