Are they large rivers with fast water or big slow moving rivers? When I first got into kayaks I bought two. An Old Town 2 person 16' kayak and a one person 9' Swifty Perception. Both were needed since I did both types of water. The Old Town was great for lakes and big rivers, though I did use it in places that it wasn't designed for from time to time and the Swifty was for smaller faster water. The big kayak was efficient and fast on bigger water, though not as fast as a Dagger or other higher performance type kayak, but it was also more stable and forgiving, perfect for a beginner. The Swifty was also more stable than a dagger type but could turn on a dime, downside to that one was it was slow on big water or lakes. For a starter boat get something a little more stable and forgiving but not too expensive, meaning it may be a little heavier, a little klunkier. If you like it, you can upgrade in a few years. If you don't you aren't out much money.
On another note, get a good paddle that fits you, don't skimp on the paddle!