Flight
This is the closest airport. We prefer to fly Delta, yay for Coke and Biscoff cookies! Our best suggestion for affordable flights is to check Kayak.com or set a "Google Alert" for the flight date and your phone can alert you as to price changes/suggestions as to when to purchase.
Rental Car
We use Kayak to easily compare car rental prices but feel free to use whatever website you'd like! I'd suggest something that is more gas efficient as Atlanta is best known for our traffic! :) Also, try to get gas outside the perimeter of the city. The more prevalent the area, the more expensive the gas will be.
House Or Rental
Jack and I love using Airbnb when we travel. If you book ahead of time, you can find entire apartments or houses for private stays at great and affordable prices. Much more affordable than most hotels. We suggest always booking private stays without sharing the apartment/house with anyone else, even the host. Search tips: our wedding venue is in Woodstock, GA. If you'd like to stay near the venue, you can search "Woodstock, GA, Roswell, GA, Marietta, GA" If you prefer to stay in Atlanta (which is better for the sites but about 35-40 mins from the wedding venue, we suggest searching Midtown Atlanta, Buckhead, or even Smyrna (a 12 min drive to Atlanta but less busy.)
Train
This is the "subway style" train in Atlanta but this will only be useful if you stay within the "perimeter" of Atlanta and want to be able to get around within Atlanta only. Otherwise if you take this train outside the perimeter, things are usually not walking distance. This works best if you rent/book a hotel in Atlanta and want to get around to see the sites. We don't really suggest using this if you can avoid it, especially at night.