You're all set. Your shirts sound fine. If they have a small thread count you may worries about your logo getting distorted.
But in most cases if the right stabilizer is used it will hold everything together.
As for the logo, a high res jepg with as little colors as possible will do fine. They will have software to convert it.
Nooooo. No auto
conversion. You want it to be digitized, not converted. A vast difference. The difference between live trace/power trace and manually tracing it with the pen tool. I can't tell you how many bad production files have come from auto conversion. The actually end look may be decent (I stress "may" here, even the expensive software I have will still mess up on the visual look if I let it convert to embroidery and if you don't know how to fix it, it will look bad embroidered), but the pattern itself might take 40 minutes to stitch out versus 20 (or less) due to lack of proper pathing. This happens and most people, even embroiderers don't realize that they are loosing money on the production floor (which is more money, then spending a little more on the one time fee of digitizing).
With regard to the amount of colors. That isn't an issue versus size and thickness of the objects of the design. Even if your machine only has 15 needles (translates to 15 colors), all you have to do is enter in a stop code and swap out the pre-determined slots for the new colors or some machines will stop for you already and tell you where to put the new colors. Yes, doing that extra bit will more then likely cost extra, but it can be done and easily, those that don't usually don't want to mess with it. I've done up to 22 colors for one pattern for a hat.
If they have a small thread count you may worries about your logo getting distorted. colour fades are nice when printed but are not able to be embroidered.
Actually they can look nice.
Attached are some that I've done. There are limitations to this though, but they can be done and can be done to look nice.
With regard to small stitch counts, that's not actually correct. If you have distortion, it's typically due to hooping technique, not enough (or right) type of stabilizer, or poor digitizing. Not utilizing underlay, stitch angles, and push compensations correctly depending on the type of fabric uses. Yes, type of fabric/weave plays an important part, which is why "one size" doesn't fit all with an embroidery pattern. Sometimes different needles, stabilizer and/or machine speeds can help, don't get me wrong, but it isn't advisable. However, if you are going to use multiple fabrics (and say hats as well (or think that you will eventually)), let the digitizer know now as it's easier to try to compensate for everything now, then it is later on after destroying garments. Think of an embroidery pattern as a printer profile.
Moze about your logo specifically:
For a normal logo crest. I would be worried about the size of "Sign Services". Thin small text (while it is block, which is good), doesn't really translate well, unless your embroidery shop also slows the machine down, uses a 65/9 needle and a lighter weight thread (which is available in white). Even then there might be some issues. Most don't like to change out though. This is just an initial look though, I would need to put it in my software to measure it at 1:1.
Now, I know I showed blends, but in this case, it won't work. The blend goes into too many objects that would actually look better as satin stitches, not fills. If you notice where I did the blending in the attached photos, those are fill stitches, not satin.
Beveling, like already mentioned, is going to need to go. Beveling and drop shadows, do not translate well into embroidery, regardless of how well they have been digitized.
The measure tick marks will also need to go, unless you want them to be running stitches, not really all that nice looking compared to satin stitches, but they do have their place. Just not here.
As to file formats, EPS 3 or 8 are safe as any high res raster file. One thing you have to keep in mind is that gradient information in vector formats doesn't translate into the embroidery view, if you want gradients or blends to be seen, it will have to be a high res raster file. It has to do with how the program does auto conversion, this is probably why some people think you can't do blends. It doesn't translate well through auto conversion, because vectors (which are typically the safest for auto conversion versus raster files) with gradients aren't typically read as efficiently by digitizing software (or sometimes totally ignored).
Now Moze, one thing that I would add out of concern for your comment here:
. I'm going to use a local shop, so they'll obviously know what's needed but I'd like to get a little educated ahead of time.
That's not always the case. Just like the sign industry, there are a lot out there that don't know what's going on. Why something doesn't look good, or why you wouldn't do this, that or the other etc.
EDIT to Add: I noticed the garments that you bought, if you bought the thin stuff, stabilizing and digitizing are even more important. Certain stitch angles on weaves without the proper amount of stabilizer will cause the fabric to do what we call "spooning". The pattern will be too dense and the center will bow inward and the edges will curl upward (like a spoon). This isn't good. Enough light weight tear away stabilizer can mitigate a stitch heavy design (yours will have quite a bit of fill stitching in it), but if those angles are at the same angles as the weave, it will take a lot of stabilizer to mitigate that.