Find a really good running store. They can help you find a shoe that works with your body. Your feet probably strike differently than the next person.
We have a small professional runners chain here called Fleet Feet. They will even put you on a treadmill in the store and do a free gait analysis to see if you pronate or supinate your feet.
The new trend seems to be ultralight shoes. I used to run competitively and I always preferred a very heavy very well cushioned training shoe. That way I didn't get as beat up and my race flats felt wicked light. New shoes need to be broken in. If you're just starting out do a couple miles a day for a week until you, and your shoes, start to get used to it.
Previous & still favorite trainer: Nike Air Max 95' ($140-ish, MANY colors available, Big chains like FinishLine carry them usually)
You want the ones with the separate air chambers, not the whole long footbed.
This.
Not this:
A bit heavy but massively cushioned shoe. You can still buy this shoe as it has become a fashion item in new colors every season. I think it's a great shoe and I never had issues running 60+ miles a week. The only downside to this shoe was that I would kill a pair fairly quickly. I always seemed to flatten an airbag every three months or so. BUT.... I had no back, knee, or hip issues so I felt the high price was justified.
Current trainer: Brooks Adrenaline GTS 12 ($120-ish)
This is more of a support type shoe and is getting towards that ultralight feeling shoe. I don't run as much and I don't race often anymore. Fleet feet does not carry Nike so I decided to try a pair of these. So far so good but it's winter and im on the treadmill so I don't know how they are going to be once I can actually be out and hit the pavement in them. The treadmill has a fairly cushioned belt so body stress will be different in a couple months when I'm outside.
Race flats - You don't need em' unless you race... a lot. Totally personal preference and fit. Mine destroyed my feet but I won a lot so I dealt with it. Usually run pins for road courses and 3/8" spikes for cross country/trail courses. I always ran some type of spike even when everyone else was running in a waffle or blanks. I liked the extra grip and the intimidation factor. "Clicking" up on someone across a road gap makes them check their shoulder.
Training: If you're unsure of your mile pace try and get up to around 45-60 min of continuous running where you are working 75% of your max. Should be a good training interval. 7-8 min/mile is pretty decent if you really want to get in shape. A local high school track is a good place to start out and get an idea for pacing. 4 times around the inside lane is just about a mile. Time yourself and you can get an idea for how fast you are going and what feels decent/strenuous. 5 miles is a decent training run.
. i believe the marine pt test is like 3 miles but of course you're gonna want to train for more. saucony and asics are a good running shoe. like nix said, find a store that specializes in running/cross training, they'll be able to hook you up.