You are wise to invest in tummy time for your son. It will do all the things you are concerned about and MUCH more. Tummy time is CRITICAL to brain development and to mobility. I spend much of my professional time helping families whose children did not get the amount of tummy time they needed. BTW, you should push for every possible moment on his tummy. It is truly THAT important.
Some suggestions to help:
Consider getting a piece of naugahyde on the floor so he will have something that is soft, yet he can easily push off with his feet. Once is he moving around, his frustration will be much less.
Also consider that babies do not have very strong respiration yet, their crying is sometimes a way to rev up their respiration so their muscles have enough oxygen to move. It's similar to how you take some deep breaths before you attempt a big physical feat.
Be on the floor with him and reward him with tons of affections and spinning and twirling and up and down when you pick him up. Tell him how great it is for him to be learning to move his arms and legs and how great it's going to be when he can motor all around the house.
If he can be there for five minutes, try to encourage him to be there just a little bit longer each day. Give him MANY MANY opportunities each day---even twenty plus. As you gradually increase the amount of time he is on his stomach moving (or learning to move), you can gradually decrease the number of session.
Please feel free to email me if you want more information or help with this. I would be glad to do so.
D., Mom to 8