If you are just paddling lakes and streams, and not fishing, the sit-in boats may be a better option. They are actually more stable and easier to paddle through the water, and can be less expensive. You might take a look at the Old Town Vapor series. I have a Loon 100 that is an older sit in boat from Old Town, and it is my favorite kayak to paddle in lakes and ponds and slower streams. I even modified it for fishing eventually, but it's primarily a touring kayak.
There are a lot of decent boats in the $300-$400 range, anything that is rotomold or otherwise one piece construction should be acceptable. The ideal general size range is 10-12 feet, with 10 feet being more practical to car-top or toss in a truck bed.
Keep in mind you'll also need at minimum a paddle and a PFD to go with it. Paddles can be cheap, but any serious paddler quickly finds a lightweight fiberglass and/or carbon fiber paddle is worth the cost. The difference between working a 40oz aluminum and plastic paddle and a 20oz carbon fiber paddle is huge after a few thousand strokes of paddling. You can get a basic carbon fiber shaft paddle with fiberglass blades for around $100 that will be 25oz or so. Most male paddlers use a 230-240cm paddle, some shorter persons might go to 220 or even 210.