Probably the two most important basic things:
DISTANCE:First you need to know what distance your horse would prefer. This can be a bit of trial and error, but your jockey feedback will tell you if the horse wants further/shorter or not. At the start use your Breeding Indicator distance as a guide and then your jockey feedback if the Breeding Distance isn't working.
The horse's stamina bar might be an indicator - IF the Distance Adaptability ability is decent. If the Stamina bar is at 100%, your horse could race over 2m4f. If it's 50%, I'd usually say that's 1m2f. 10% is probably 5f or 6f. However, I've sometimes found that a horse has no Distance Adaptability rating, so despite having buckets of stamina, couldn't race effectively not at their Breeding Distance.
CLASS:Maidens - for horses yet to win.
Handicaps - each horse carries a certain amount of weight depending on their rating. The more highly rated you are, the more weight you'd have to carry
Conditions - horses race off level weights, but these tend to be pretty poorly contested as prize money isn't great
Listed - for horses that are too good to be racing in handicap races but not ready for Group races.
Group - Groups 3, 2, 1. The best of the best. Group 1 is the best horses, Group 2 is slightly down from that and Group 3 is slightly down from that.
Personally, I tend to progress my horses steadily. Starting with a maiden, then a handicap or conditions race. If they're winning, then I'll go to Listed and to Group races. Every now and then you'll have a horse who is the absolute business and you could go straight to Group races with. Again, your jockey will tell you if the horse is out-classed or needs to race in a higher class.