A horse does not HAVE to have a show record to be a reasonable breeding prospect.
The Olympian I went to work for for a week has 70+ broodmares, NONE of which are broke to saddle or have EVER seen the inside of a show ring. They ALL have outstanding bloodlines and produce stunning foals, but despite their bloodlines, conformation etc and the bloodlines and conformation of the stallions they STILL occasionally drop average foals.
They haven't had a mediocre foal, EVER, but average is not unusual. That's from TOP bloodlines!! They have some truly superb youngstock there, some good youngstock, and some average youngstock, all from his own top quality mares and stallions.
Breeding is a gamble at best. You should breed THE ABSOLUTE BEST mare to the absolute best stallion you can get your hands on, and if you can't get your hands on horses of superior quality, don't even go there. The average person can breed a horse, nothing wrong with that, but your chances of getting a fugly are so much higher if you use average to mediocre horses for breeding.
The market is rubbish atm, why breed for ANOTHER "just a paint" when you COULD give it your best shot at a world beater? "I'll never sell it" is simply not a reason, either, because you never know what the future holds, and circumstances might very well force you to sell (and sell quick) - so why not breed for the best possible foal and give it the best possible chance of a good home, and fast?
Note, I know NOTHING about your mare, so I couldn't say if she is or isn't breeding quality... just be aware that cheap stallions are cheap for a reason, and most of them should be avoided. A GOOD stud will set you back (here in Aus) anywhere from $1500 upwards. I have seen stallions with fees in excess of $5000 and TB stallions often fetch $80,000 PER COVERING. Especially the greats!
And stud fee isn't the least of it either! There's preg checks and ultrasounds, feed for the pregnant/lactating mare, the foal (before weaning and then more so afterwards) until it's all grown up and ready to break..... it's quite common for foals to cost $10,000+ from covering to breaking, or more!
...if it was ME, I would just be buying a weanling or a 3-4yo. You know what you're getting then!