Being in southeastern Idaho with Idaho Falls the only major urban area nearby, you won't be expected to spend too much on rent in Ammon. Frankly, that's fair, given that you'll be unlikely to earn the big bucks you'd get over on the east or west coasts. You're not going to find dozens upon dozens of high-rise buildings with rental apartments either, so be prepared to expect only a handful of potential properties that will suit you and your needs.
As you might expect, prices will rise during the summer months, so moving during winter might help you save a buck. Vacancy rates, however, are often lower during those times, and you'll be more likely to come up against stiff competition. Give yourself an edge by getting your paperwork sorted early, so that references, employment letters and the like are all ready to be handed straight to the agent or landlord.
Ammon is dominated by greenery, and there are only three neighborhoods of mention in the city. This gives you few options to choose from - but, on the plus side, will prevent you from umming and ahhing too much over which area to choose.
S 45th E / 1st Street: Lots of three- to five-bedroom homes stand here, with a handful of apartment buildings for good measure. There is a pretty big Walmart to the west, which will certainly help you kill two birds with one stone if you want to pick up dinner and a television for your new home.
City Center: There are a few nice parks here, along with a mall on the western edge, where you can satisfy any shopping urges that you may have. There's also a nice restaurant -- the Cellar -- with a real focus on good wine!
S 25th E / E Sunnyside Road: There are a few more apartment buildings here, so if you're looking for studio apartments for rent in Ammon, this will be the neighborhood for you. If you like a bit of rodeo entertainment, you'll also find Sandy Downs Arena here, too.
Ammon is known for its wide open spaces and parks. There are nine in total, covering more than 60 acres, so that means you'll have plenty of space to walk your dogs and take a stroll in the spring and summer. McCowin Park is the biggest and best, with ball fields, a disc golf course, walking trails, tennis courts and a swimming pool to enjoy. You'll also be living within easy distance of some great places for outdoor activities and adventure, such as Yellowstone National Park and Grand Teton National Park. Public transport is occasionally used, mainly in the form of buses, but this is generally to get to work in towns beyond the city's boundaries, such as Idaho Falls.