I would like to add a few things regarding strumming technique to Hrodelbert's answer.
I find that many beginning guitarist have a difficult time with smooth strumming. It's normal and over time and with proper practice, your strumming will improve dramatically.
Certainly the position of the guitar relative to your body can have a big impact. But there are some other things to keep in mind as you continue to practice and improve your strumming technique.
First, for basic strumming, be sure to properly anchor your strumming arm on the body of the guitar. For most folks with most acoustic guitars, the anchor point will be with your forearm contacting the guitar body near the top of the lower bout (widest section of body behind the bridge). Electric guitars will differ depending on the body shape. Anchoring your strumming arm in this way will keep your angle of attack consistent, and the orientation of the guitar (vertical to floor or tilted slightly back to see the frets) will have less of an impact than if your arm is free to wildly flail about.
It is important to avoid the temptation to use your elbow as a "pivot point" for swinging your arm. Unless you want to get "guitarist elbow" (same as "tennis elbow") you don't want all of your up and down strumming motion to come from movement of your forearm.
Instead, try to relax your wrist and use your wrist to strum up and down - not your entire forearm. Try to imagine using a paintbrush to paint a wall with up and down strokes. You will alternate the angle of your wrist and the brush (pick) according to the direction your wrist is moving (up or down). Also, the smaller amount of movement required by keeping your forearm anchored and strumming with mostly wrist, will give you greater control.
This technique will take practice but soon you will get a smooth, rhythmic, and controlled up and down strumming motion - with very little stress on the tendons in your elbow and forearm.
Another thing you might want to experiment with is different gauge picks. Most beginners find it easier to strum with lighter gauge picks. As you get better at strumming, you may want to try medium or heavier picks.
Before trying to learn advanced strumming techniques, I would encourage you to hone your basic strumming technique with a goal of smooth, consistent, strumming. Before long you will be ready to move to more advance techniques such as palm muting and percussive strumming.
I wish you the best of luck as you continue your journey towards a life long passion of making music with your guitar.