Bigger or smaller repair shops -- dealership vs independent -- have more to do with the wherewithal to invest in more equipment and hire more mechanics because you already have a larger market share and it is growing. The key to running a successful shop -- big or small -- is to maintain a regular, growing customer-base which loyally continues to return for more service because there is some level of trust.
I don't know if ALLEN TIRE is nationwide or regional as a chain, but I started going to them immediately after purchasing my first Trooper in 1999/2000 (the '87) and continued with them through brake repairs, tire and shock replacements with the possibility that more serious front-end or suspension work needs attention.
You should always balance and align your wheels after replacement of old tires for new. If they charge -- and Allen does -- its one-time and chump-change for the life of tires that may have cost you at least $500. (Mine are more.)
I have a sense of trust with the local Allen manager. With or without it, they offer free periodic balancing, rotation and nitrogen-gas inflation services as part of the warranty provisions for a sale of new tires. The tire prices are always reasonable. And they will even give you a choice to purchase tires at COSTCO so that Allen takes possession and installs them.
For the rest of it, growing up building your own skateboards, riding and fixing your bicycle, pushing shopping-carts and other activities, you should have a sense whether your tires are "right" or "wrong" for something like a tire balance. A symptom for being out of alignment might be instances when the car seems to wander in one direction. Out-of-balance may be indicated by a vibration that increases in frequency with velocity. You can look at your tread depth with a Lincoln penny or something better, and you can identify patterns of abnormal wear. I don't enjoy riding along with square Flintstone stone wheels, so I don't defer, I don't delay -- it's routine maintenance cost which you should simply budget on an annual basis out of your income -- or from other resources, but I follow my own rule.
That leaves steering-wheel freeplay. Before you let a mechanic tell you that your freeplay is too loose, consult the factory manual for the adjustment spec and go for a roadtest to see if you are within that spec or just equal to it. You can adjust the steering-wheel freeplay most likely with a wrench applied to a single hex-nut (->shop manual), or arrange for a mechanic to provide his opinion and do it for you.