Decide also if you want to breed for utility (egg laying ability/ meat production) or for show (feather pattern and overall conformation to Poultry Society standards). There are more show breeders than utility breeders it seems! It would be great to get more utility breeders, and as you've already pointed out, Hampshire Red are a brilliant utility breed.
Once you get chicks underway, to find out how good the utility qualities of your birds are, you would ideally need to keep records of weight gain/month, age at first egg laid and number of eggs in the first/second year. You would then keep your best birds for breeding on and cull out undesirable traits such as poor egg production (or keep as pet quality, but don't breed from them).
If you're serious about starting up a breeding flock, you'll definitely need more chickens! It's by no means for sure that the birds you have are good examples of the breed. I was advised by the lady at Kintaline Poultry Farm (they have an excellent website and lots of utility breeds) to get a dozen hatching eggs from as many breeders as I had space to raise, take the best growers and put them into trios/fours and keep records on the chicks produced.
Broody hens raise healthier chicks than those reared in an incubator (generally), downside iis you have to wait for them to go broody. Unless you get a Silkie or a Pekin, which seem to be permanently broody, I gather!