If you have TAS, it's going to get a lot worse once you start kayak fishing! Although practically anything will get you out there and in to a few fish, safety is a consideration, so don't go too cheap. I understand you don't want to go Rolls Royce on a first yak, but compared to boats, even the top end yaks are cheap as chips. If you really get in to it, you'll want to upgrade quite quickly.
My take on it is that Ocean Kayak (OK) were the leader of the pack for quite some time, but Viking really have taken the market. They have produced some great yaks with genuinely innovative and useful extras. As a result, there are a lot of good OK models going secondhand. Anything "Prowler" will be up to the job. On the Viking side, the Profish series are the one to look for.
If you want new and budget, I have only heard good things about the Phoenix Kayaks Hornet, but have no personal experience.
Good choice on soft baiting from the yak, it's an ideal platform. You will catch a lot of fish (eventually!).