Best thing is to get fitted at a true running shoe store. They may not fit you with the perfect shoe, but it'll be a good start. Most also offer full refunds for 30 days in case you decide you hate the shoes after a couple of runs.
Some of the more popular shoes: asics GT 1000 or 2000, brooks ghost, mizuno wave riders, saucony ride just to name a few. But there are honestly tons of good shoes out there. You can eliminate a lot of them just by trying them on for 30 seconds.
If you're just starting out be aware the shoe you love today may be a shoe you hate 12 months from now. Your running style may change a lot as you get in better shape, get faster, etc.
And a little info on shoes in general. For whatever reason they "update" almost every year. So this year you may buy the Mizuno wave rider 16. You go back to get another pair in a few months and they have the wave rider 17. It may feel almost identical to the 16, or it could be a completely different shoe. Don't just blindly buy the new version without trying it on. Also, the "old" versions go on clearance when the new ones are released. So you can get practically the same shoe for about 25% less if you buy last years model. Once I find a shoe I love, I'll wait till it goes on clearance & stock up. I've got three unopened boxes of shoes in my closet now.
One last piece of advice - get some good socks while you're at it. I'd highly recommend Balega hidden comfort. They're about $12 / pair but I've never got a blister in the 3 years I've been running in them.