How-to: open bar and alcohol for your wedding
You need a bunch of "standard" decorations for your bar. You can get them at any regular grocery store. Limes, lemons and mint need to be bought a day or two before the wedding. Course cane sugar is great to go with Mojitos. Olives & red cherries are great for transparent drinks.
Straws, toothpicks are also easy to get in a local store.
This part is important and is often overlooked or under-invested by the hosts. Get this especially if you have any pregnant friends, small children or older family members coming, and ensure there are plenty of non-alcoholic options.
Your easiest bet is to have your caterer deliver fresh juices and sodas. If your caterer is not delivering those for you, you can get those at any store - just keep in mind that even your friends who drink a lot will also need to drink non-alcoholic options. Plus your juices and sodas will end up in all kinds of mixed alcoholic cocktails, so GET A TON of these.
Easy - bring a cooler, have your caterer pick up a few bags of fresh ice on the way. Have the ice cooler sit next to the bottles of alcohol. Smaller cubes are preferred to larger cubes. Have a scoop handy for people to get ice cubes for their drinks "on the rocks" (we've gotten a few questions on this before - "on the rocks" means "with whole pieces of ice").
Strainers, stirrers and special glasses
If you're not hiring a pro, just buy a box with everything you need. It'll still be cheaper than hiring a bartender, and let's face it - you're still young - so unless you completely do not drink any alcohol, you can safely assume a kit like this will make entertaining your guests more fun even in your married life.
As a state-licensed bartender, I'd recommend 10-Piece Cocktail Shaker and Bar Tool Set (I actually own these) or something more elaborate like The Ultimate Home Bar Kit if you think you are likely to host more parties in the future (of course you will!).
No, don't get cheap college beer-pong Costco cups. Instead, opt for transparent tumblers - also sold at Costco or some local grocery stores. They look pretty cool and are not that expensive. You do not want to have real, fragile, thin glass next to a ton of drunken people. It's not fun to see anyone bleeding at your wedding when a glass falls and breaks, and someone gets cut by accident. Plus renting glassware is just not too cost-effective.