Where do you live again? Near Peoria? If you want to get together and shoot at a fairly nice outdoor range, let me know well ahead of time and we can go to my club. It's in Springfield, but that's not a bad drive.
No Class 3, but you can rent machine guns at Law's range which is pretty near you if I recall correctly.
http://www.lawoutdoorrangeandguns.com is in Chandlerville, near Virginia.
Do NOT screw around with the waiting periods. They DO put people in prison in this state both for getting guns too soon and for allowing their friends and neighbors to take possession too quickly. It happened in, I believe, Lake County last year. Guy sold an SAR-1 to his neighbor he'd known for years and let him take it that day. Figured it was only going next door and he knew the neighbor was a good guy. Went to prison. Is now a felon. WAIT unless you're practicing civil disobedience.
Do NOT have a loaded gun on your person or in your car outside your property, a range, or a hunting situation. You MAY transport legally on your person or in your car as long as the gun is unloaded and in a case. Those are the only requirements. You can have a loaded magazine right next to it in the case, but no rounds in the gun. The case can be any case, box, container, etc. that completely encloses the gun. A holster is NOT a case. A fanny pack, day planner, CD case, backpack, cardboard box etc. would be a case under the law.
Have fun! And join as many pro-gun orgs as you can. CCRA and Concealed Carry Inc. are the most effective, but that's not saying much in Illinois.
http://www.gunssavelife.com
http://www.concealcarry.org
http://www.isra.org