Having overhauled, rehabilitated and serviced MANY wheels in the past few years, I mostly agree with
branko_76 list. More is better and I both doubt a) the LBS will do all that is needed and have the skills to do so and b) you could afford the hours it takes them to. But the Utah winter is coming along soon so this is a great time to learn wheels. Get them ready for spring.
Having rehabilitated numerous vintage wheels, I would
- mount the wheels in a stand, a truing stand or something similar.
- place a drop of light oil (penetrant, mineral oil, 3 in 1, TriFlow) on each end of each spoke nipple.
- spin the wheel numerous times to get centrifugal force working the oil into the threads and the nipple rim interface.
- after a few days, fully detension the wheel to ensure all nipples turn freely and smoothly.
- inspect the rim and decide how flat and round it is. This is hard. Fully unbuild the wheel as discussed above if you're not sure. The rim must be flat and round. Clean and polish the hub and rim to your satisfaction. I don't do much of this as all my bikes are riders and the wheels get spooged up quickly anyway. I just want clean and presentable.
- slowly and evenly retension the wheel, keep an eye on runout, dish and hop as you progress. Correct along the way to keep things easier as you close in on done. Yup, you now need a truing stand or a viable alternative. Lots of threads here on alternatives. My stand is home made.
- read up a lot of final truing and tensioning. Too much to explain here. It takes me several days ( not many hours/day) and a few hours. I enjoy it and do get excited about 40 year old wheels. I could never afford the LBS bill to have them do it. It would be a couple of car payments.
If you look for an LBS to do all this, read up a LOT on how to do it so you'll know if they DO know how to do it properly. Be fussy and specific. Some shops will hand this to the least experienced wrench. You don't want that and you need to know how to evaluate their experience and standards of excellence. Talk is cheap, as we all know if these unprecedented times.
BTW, I'm in the freewheel total overhaul camp vs the "flush er out and drool some awl in" camp. I've seen too much. My LBS throws the in-op free wheels in the recycling and installs new. I doubt they even know how to overhaul one.