Holliday,
Most runners wear a pair of shoes for training and another for racing. Most runners have learned to run striking on their heels because most shoes tend to force you to land that way. If you watch little kids run around without shoes, you will notice they land on the pad of the foot behind the toes. If you are lucky enough to still run like that, you can get by with a much lighter shoe than if you strike on your heel.
How do you know where your foot strikes when you run? Try looking at the bottom of your current or past running shoes. You should see that a certain part is more worn down than the rest. For most of us, that is the outside edge of the heel. That pattern is called, I believe, pronation. If the wear is more towards the center outside of the heel, that is considered neutral. If the wear is on the inside edge of the heel, then it is consdidered (if I am remember the terms after all these years) supination.
You can look in "Runners World" Magazine or some of the online shoe stores like "Road Rnners Sports" and get a general discription and a sizing chart. A good running store is an even better bet. A true running shoe store's Salespeople should be able to look at your old running shoes, watch you run a few steps, and tell what kind of shoe you need.
If you are a conventional heel striker (pronator, neutral or supinator), you may be best served by having a pair of training shoes and a pair of race shoes. They don't have to be mega expensive. I always got by with some midrange trainers like the ASICS GEL 2040 (OK started with the ASICS Gel 110 back in 1989). I always raced in the lightest spikes I could find. I can't remember the name now but there are tons out there. The reason I chose spikes over racing flats is that you can put in various lengths of spikes depending on the ground condition. If the ground is soft and slippery, longer spikes. If it is hard and firm, screw in some short, flat spikes that fill the holes but don't even reach past the sole of the shoe. They just keep the holes that you screw the spikes into clean.
If you are one of the rare and lucky individuals who are POSE runners and land on the pad/ball of your foot, you should go with a much lighter shoe with considerably less heel support than the average Asics or Nike. Mizuno has a number of the "Wave" series of shoes that fill the bill. They get more expensive and considerably lighter as you go up the product line. I would not advise getting the lightest most top end versions for cross country as they are so light, they offer almost no protection for your foot and are too soft for the debris and rough stuff you find on a typical cross country run. I have the top of the line Mizuno Wave shoe and it is incredibly light but is only suitable for running on roads and maybe manicured golf courses, etc.
www.crossfitendurance.com has some advise on good trail and running shoes for POSE runners; far more than I can give.
Hope this helps.