Change the oil and filter first, I'd go with 10w30, then see where you are. Make sure the old oil doesn't look like it's coolant contaminated or anything...if so you've got bigger problems.
If all looks good, and the light still persists, I'd change the sender just to rule it out....if it still does it, chances are you're dealing with a badly worn oil pump or main bearings, or a partially clogged oil pickup screen...all costly to replace. But generally if this were the case, you'd hear a lotta racket too while it's running cold with the light on...are you?
If that was the problem, I'd consider Lucas or something like that if I didn't want to shell out for a big bottom end repair...
Edit to add a thought....I have had some luck on cars with clogged oil pickups running a mild solvent like Marvel Mystery Oil or in extreme cases, kerosene, through them. Kerosene is pretty dicey, I only do it to engines that are terminal if that doesn't fix it...Add a 1 quart of it to the oil that's in it, run it for about 15 minutes, then drain the crankcase completely, fill with new oil, and drive no more than a couple hundred miles and change the oil again to get any remnants out...but it does open up a clog, most times...