How must rest between workouts?

Congrats on starting the gym and doing lifting!

That being said, skip the advil and try every other day or just 3 days a week. I used to go 4-5 days a week when I first started and I was tired, sore and miserable all the time. Having at least 1 day of rest in fantastic. Plus you won't get burned out by being at the gym all the time. I just go Mon-Wed-Fri and I see fantastic results. Granted YMMV.

I say skip the advil because it's really not going to help, plus trying to mask any pain/soreness you have could ultimately result in injury from not doing lifts properly. Learning to work through soreness is important and once you get warmed up it goes away, if not or it gets worse then that should be telling you something.

Making sure you're getting enough protein will help with the soreness tremendously. I don't want to sound like I'm on the Bro-Science train but the second I actually started paying attention to that I noticed an immediate difference in severity and length of time.

Don't have to consume some rediculous amount either. I aim for 1g per pound of lean body mass, I'm sure I eat more than is actually needed though.

Protein Synthesis takes 48-72 hours. You should never work the same muscle group on consecutive days. As already stated, your body will adapt the more you lift and the DOMS will either be less or go away completely.

^This