1999 Ford Taurus oil change?

I've never changed my oil myself but since jiffy lube messed my car up before I decided to try it myself. I was wondering after you drain the oil and go to remove the filter do I need to have anything covering my starter or if the last of the oil will miss it when I remove it? I know oil has messed up my starter before but that s when there was plenty of oil in there.

Shouldn't get much oil on the starter if the system is drained, you can put a shop towel over it if needed. Just make sure to torque the drain plug enough and a lot of people recommend adding some oil into the filter before you install it. Big thing is to ENSURE the rubber gasket from the old filter came out with it and isn't stuck onto the filter housing because that will blow all your new oil all over the place really quick.
The old filter will be full of oil so try to not tip it over so it spills much. And yeah, a WARM engine is better to drain oil from but isn't needed, just don't let temps get to where you're at risk for dropping something hotter than expected.

That's a good call - I don't trust anyone with my car.

I've seen oil change places underfill, overfill, fail to change the filter (while still charging for a new one), etc. (and that's before you get to overcharging, and trying to sell you on other unnecessary services and parts).

As far as your starter - it's a good idea to cover it with a rag or something if you are concerned about oil running down into it.