96 Es300 - Problems Starting And Sensor Problem

[godlyman]

I've been having some problems starting my '96 ES300. Sometimes when starting it, it wouldn't turn over. The radio and AC would come on, but that was it. If I turn it off and let it sit for a minute, then it'll start. It would work fine while driving and everything worked after it started. I took it to AutoZone for a free check. A guy put a tester on the battery and I could see that it said: "bad battery". The battery is only maybe a couple of years old. He said that the problem is probably that the alternator needs to be replaced. I can take my car back to the shop where I bought the battery since it's still under the 5-yr. warranty to maybe have them replace it (again). Should I also have the alternator replaced?

Also, the check engine light has came on. I don't know if this is related or not. I had AutoZone check that, too, and was told that the problem is: "P0150 - Heated Oxygen Sensor Circuit Malfunction". Is it OK to drive or is it critical that I get this replaced right away? Thanks.