Diane,
We regularly embroider on knits as light as 4 oz. Be they golf shirts or t-shirts, it is still a knit vs. a woven.
If you are looking to have garments embroidered I would consider this, treat the process as three separate steps with three separate vendors.
1. Buy your garments from a garment supplier.
2. Have your artwork digitized by a professional digitizer.
3. Have the garments embroidered by a contract embroiderer.
IF you can combine these steps with one or two vendors, fine, but it is not a requirement. There can be advantages to one stop shopping but sometimes it just doesn't work out. I personally prefer to deal with professionals in each of the three steps and by doing so I am in control of the process from beginning to end. Even though we embroider and digitize in-house, there are times where we outsource all or part of the process. Obviouesly, we buy garments from a number of manufacturers and wholesalers. We use six different digitizers on occasion, two for our overnight overflow work with basic logos, one for tiny lettering, one for fins, feathers and fur, one for extreme detail and one for multi media jacket backs. We use two contract screen printers and a couple of contract embroiderers and we use a few specialized full service shops like Carolina Caps.
There are vendors that excel at one stop servce. Vantage Apparel sells fantastic garments and has a top notch decorating department. Carolina caps provide great custom caps and their decorating quality is very good. I'm sure there are many others. But for every one full service contract shop, there are dozens of shops that do one thing very, very well.
Don't be so hung up on "Local" embroiderers. Seek out contract decorators and they should be shops that ONLY do contract work, not shops that are predominantly your competitors but take in contract work to stay busy. If they are local, fine, but if not that's OK too. Internet, e-mail, phone and fax can cover a lot of distance in a hurry. Just be mindful of additional freight costs. Lots of contract shops provide free pickup from the major garment distributors to help out in that area.
One last note, there are no standard policies. Just so there are policies and both parties agree, that's what is important. In your dealings with contract shops it should be obvious that they exist to serve their contract customers and that will be obvious from the outset. They will have policies and procedures in place to move your garments in and out with little effort and no opportunities for ambiguity. Look at places like Target Graphics, Vantage apparel, Minds Eye Graphics... they all have very clearly established policies, price lists etc.
Good luck...