Let’s start with the shoe type; first you must consider what type of running you are looking to do. Do you want to run trails or roads? Do you plan on running competitively in races?
Trail Shoes have specific soles made to grip the rocks and dirt to prevent you from sliding, and the write cushion and materials to make it so you don’t feel these rocks on your feet.
Road Shoes are made with less aggressive soles that work better for gripping the road and not wearing out quickly when used on asphalt daily.
Racers are made specifically for racing; I highly suggest not using them for daily runs. They are lightweight and more likely to wear out quickly when used daily. They don’t have the same kinds of cushion and stability that a road or trail shoe have, which means you could potentially get injured if you wear them for your daily runs. Racers are great as a secondary shoe for those looking to compete in races.
Cross Trainers…I typically tell people to steer clear of these. This is the marketing world’s attempt to make a “one shoe fits all” option. You won’t find the specific needs for daily running with these.