I am shorthorn enthusiast who is greatly involved with the lot-feeding steers for carcase competitions. I understand you are not into the show aspect but our feedlot has been using predominantly shorthorn steers for the entire 20 years of our existance. Over the years we have won many championships with both purebred and crosdbred shorties.
In my experience, shorthorns have excellent temperements, making them easy to handle and halter-break, and ideal for someone who is not particularly large, strong or extremely experienced. Shorties tend to grow out at an excellent rate and be ready for slaughter at a relatively early age. In my enterprise I hav recorded up an average daily weight gain of up to 3.5kg and have consistently slaughtered steers at 12 months of age. Shorthorn steers have the capacity for excellent muscling, some of my own ending up with an amazing B plus or even A minus muscle score. A steer I recently entered in a competition had an enormous eye muscle area of 100 square centimetres with a live weight of only 420 kg

almost unheard of for a shorty steer. As far as I'm concerned, as a breed shorties have very little structural faults however in the taller, leggier animals you have to watch out for a weak topline (spine) and dodgy back legs.
As far as crossbreeding goes, shorthorns are an incredibly diverse breed, being compatible with almost everything. However I would not suggest a bos indicus (tropical) breed as they seem to have a negative impact on the pros of shorthorns. In particular, angus-shorthorn and poll hereford-shorthorn crosses seem to provide top-notch carcases. An angus-shorthorn steer I took to a show last year gained an unbelievable 98 carcase points out of 100 and sold for $4.85 per kilo. A friend of mine entered a simmental-angus-shorthorn cross in a carcase comp and gained a never-before-seen 99.9 points out of 100.
Good luck with your shorthorn project and I hope this has helped.