Get a good detailed list of everything you have for the build....finished, unfinished, new and used (include part numbers and manufacturer if you have it)
This will be a great place to start because if we know what you have we can better steer you towards what you need, and what to do with all of it once in hand.
Concerning an engine shop....Right here you can find a few very good shops.
FE's are a bit tricky and the shops that are well versed in 350 Chevy small and big blocks might not know the details of properly building an FE....Lots of it is similar, but not the same as other engines.
I don't know your budget but I will inform you from direct experience....Paying up front to build the engine correctly the first time is well worth it.
If built correctly the engine will run best, give little troubles (FE's always need some petting) and basically lead to enjoying your collector car because the engine just works when you turn the key.
If built, okay, but not correctly, it is likely you will be fiddling with the engine a lot, even if it is just tiny irritances and adjustments. This can lead to frustration with your collector car and less enjoyment over time.
If built incorrectly you will be rebuilding again....and again....and yet again. At which point you will have invested enough money and time to have paid for a full race version of the street engine you have. By the way, a built incorrectly FE will run and drive at first, so it does not seem like it was rebuilt incorrectly.
Do not cheap out on this rebuild...it is not worth the "savings" in the long run.
This does not mean you have to throw money at and FE to get a good rebuild.
It means you must know what needs to be done and then do that correctly.