Will add a little value here to what is already a good start.
In the early part of the game the main thing your looking for is potential. And this comes in two forms, dark green on the bar denotes how good the horse is now, light green how good he could become, and both could improve during the horses 2yo season once you get a few runs into them. It may improve again when they turn 3yo and then again at 4yo and 5yo. This improvement maybe the filling out of the light green bar or an increase in both, there could also be no improvement at all, some horses simply do not improve. You usually know if you have a good horse by the time they are 3, the 2yo growth period and the turn to three is the most important, but some will not be at their best until 5, some maybe 6, though typically around 6 potential will start to decline. If you have a 3yo who has a potential bar in the region of say 80% of full your likely onto a horse who will be competitive at G1.
When breeding the two horses you select form the basis of the foal, and in simplistic terms you will get something that will over all stats be as high or low as the parents, with some degree of freedom. So two 80% horses will in all likelihood give you something in the same sort of range. Now early on of course the available horses you have for breeding will not likely be that good and you will also not likely have too many of them, so taking advantage of the game horses available for breeding is likely the best way to take a leap forward, pick the best available based on the breeding fees, but also look lower down for horses with a few runs or very fast times. The fee is really just based on money they have earned so a horse with 50 runs but nothing better than a G3 may cost more than a horse that only ran and won a few g1's, the later is of course the one you want to be focused on. Though you may also find said horse has undesirable qualities too, this trial and error part will lead you to wanting more horses to breed with, and as your overall stock improves your own horses will start to be more important than the gamebreds, as you have more clarity as to what your likely to get.
Money is very important to this end, but a bad horse breed, when sold at 2yo may generate a nice profit, so their is mileage in buying some cheap fillies at auction and just breeding them to sell, you also get a stud fee when you retire them from the game, I do this more often than auctions now as I hate it when I screw up and find I just sold a champion hurdle winner
The 2yo season opening auctions are often disappointing, but can very rarely throw up a good one, but if money is tight focus on the mid week auctions where you at least have a little form on which to base your choice. Using the horse tab to follow the best game horses in the hope they come up for auction is also sensible, and worst case of they retire you may get one season to bred with them through the barn. Lots of trial and error and lots of time, but once you have a barn up and running and are getting a few horses per year the money pressure side of the game diminishes.
After potential, extra speed and cruising burst are probably the most important, especially if you have longer term aspirations to play the online league, though also pay attention to finish application and consistency, but early on potential is the first hurdle to overcome.
Also as said do a forum search for breeding, there are a lot of good older posts on the subject, and plenty of very helpful players.
Hope that helps.