I love the Asics fit but the shoe you'll need is based on your pronation. If you overpronate that means your arch flattens out too much when you walk, I would try something in the Asics line with the Duomax. 1000 series, 2000 series and the Kayanos would have this feature.
The duomax is the grey area you see on the inner part of the midsole. It's a denser foam than the rest of the midsole that will help with overpronation. If you're looking for the best bang for your buck I'd go with the 2000 series. It's the most popular running shoe in the world and it is super light with a Solyte midsole instead of the heavier SpEVA on the 1000 series. It also features memory foam inside near the ankles so it's a more comfortable shoe than the 1000 series. I own both the Asics 1110 and the 2130 and they are both good shoes. But given the small price difference I would pay the extra and get the 2000 series. I find most shoes in the Asics line have a boxier area for the toes so it's more comfortable and my toes don't get scrunched up.
Older models are going to be relatively similar. So if you can find a bargain on an older model, they're not going to be much different than the current years. How Asics names their product is for example, Gel 1110 is the 11th model of the Gel 1000 series. The first digit indicates the series and the middle two digits indicate the year since the initial release of the line. The other good thing about Asics is that they come in a variety of widths. You don't want a shoe that's too narrow and uncomfortable. But on the other hand you don't want a shoe that's too wide and have your foot sliding side to side.
If you don't have any pronation problems or if you underpronate you could wear a shoe that does not feature the duomax like the Asics Nimbus. I never looked too much into this shoe since I overpronate and only buy runners with the Duomax.
I am obviously biased towards Asics because they've worked for me but also try on some New Balance, Mizunos or Saucony just to see which brand will fit your foot the best. You want a shoe with proper support and my quick test is to pick the shoe up and squeeze the heel area on both sides of the shoe. If you can easily push the heel area in, this shoe is shitty. Most of the shoes put forth by Nike, Adidas, and Reebok will do this. If you pick up a decent pair of running shoes like Asics, NB, Mizuno or Saucony, it will be reinforced in that area and you cannot push it in.