I wouldn't just go to any old place for an oil change. If you want to save money go to a reputable independent mechanic that specializes in Lexus/Toyota vehicles. Another option is find a Toyota dealership that will service Lexus cars (you have to call them first, some Toyota dealers won't service it).
As far as the alarm goes, it only goes off if the glass is broken, the door is forcibly opened (same for the trunk and moonroof), and some other situations (can't remember right now). Simply pulling the door handle will not set off the alarm, it is not that sensitive. If it is indeed broken, your car is still under warranty (unless your mileage is past the warranty), so you can go to a Lexus dealer for repairs.
I should also add that Steviej made a really good and detailed post on the tutorial section of this website on how to replace the oil and transmission fluid on a 2002 ES300. Worth a look if you're interested in doing this yourself.
Oh and btw, Welcome to the LOC. :)