I always thought of Neons as the Rodney Dangerfield of cars- they got no respect!
The dreaded head gasket problem was finally fixed by then. Neons aren't too fussy about motor oil, any decent 5w30 or 10w30 should be fine- your 05 may call for 5w20, that's OK too.
Timing belt- the 95-99 models called for timing belt replacement at 105,000 miles, I believe the 00-05 is the same. *Don't* try to stretch that- the Neons have an interference engine, & a broken T-belt will kill a few valves, maybe a piston too. When you do replace it- also replace the water pump, it's hidden behind the timing belt, & it can save you *Big* trouble later on. No foolin'- new T-belt, give it a new water pump. You've already done all the hard work then, take advantage of it.
Something I strongly recommend- put a Fail-Safe thermostat in it- they lock open when they go bad, so it doesn't overheat. Normal t-stats lock closed on failure, = overheating! On Neons, thermostat replacement is an easy quick job, and a bad case of overheating can cause a leaking head gasket. Even on the later models where the HG was no longer factory defective!
A Neon wart- the 95-99 models were infamous for the "73 mph shake", caused by being *very* sensitive to front tire balance. The 00-05 models, somewhat less so, but it's still there. If yours runs smooth, congrats! The shop that balanced the front tires did well. If you know who balanced the current smooth-running front tires, when it's time to get new tires, take it back to them.
A good forum & source of info is www Neons dot org . Hope all continues to go well, enjoy your Neon!
