First, clothes that make you feel comfortable and that you don't worry about being seen wearing, but also don't think "cool, they'll notice me in this"...it's not a bar.
UnderArmour makes great affordable workout gear that keeps you dry and comfortable, fits well and moves well. You want that.
Personally, I think compression shorts are for biking or lots of road work, but not for general lifting, so loose, comfortable gym shorts, Nike's selection is good as is Addidas. All this gear is easily found at most big box sports retailers as well as Target.
As for the bag, if you're changing at the gym, here are the essentials you need to get you feeling tight with taking your swole out for a stroll afterwards:
Roomy but not bulky gym bag, with an outside compartment for wet clothes to keep it from getting funky (A couple of dryer sheets tucked into both compartments to keep things fresh)
A clean towel
A spare shirt
Change of clothes, including both underwear and socks
A sweatshirt (sometimes gym thermostats are off kilter and you don't want to get chilled or cramped, so it's smart, just in case light weight cotton, easy off easy on)
Any toiletries like deodorant, razor, shaving gel, toothbrush, toothpaste, eye care (if you wear contacts) small bottle of bodywash (I prefer this over a bar or soap and a bottle of shampoo)
Hair product if you use it
Hair dryer if you have long hair
Baseball cap in case there's no time or you're having "that" hair day.
Flip flops for the shower...no matter how clean your gym is, trust me.
Then anything you need extra like MP3 and headphones.
The most important thing to walk in with is focus and a plan, and to walk out having done your job. The rest is icing.