Barudan bar none is the absolute best brand out there for stitch quality, as well as, support after purchase. Also, if you use their native .U?? (no, that is not a typo) files, you can do so much more within the file itself provided you are using a digitizing software (Wilcom, also the best) that allows for this. DSTs are the most common generic file used with commercial machines, but those files do not support all of the functions that a Barudan machine can do. A particular function that I use regularly on our machines is the slow/fast function. Meaning, you can speed up or slow down the machine given the needs of a particular area of the design (small lettering/detail etc) within the U?? file itself. No babysitting the machine to slow it down and/or speed it back up. Those codes are put at specific stitch points. Once the machine reads it, it does it. You can do it on the machine itself, but it's not as efficient as being able to do it within the file itself. To my knowledge that is a functionality only available on Barudan machines.
If you are wanting the same capabilities with your single head and your multi-head, you are going to want a bridge style single head. Barudan bridge style machines, with regard to caps, allow you to stitch a max of 14" wide, the height is determined by the height of the item itself as long as it doesn't go beyond the biggest size for flats. Which unless you are doing a Dr. Seuss top hat, you shouldn't hit. To give an example, on your smallest hat size (low profile, typically unstructured), I can fit a 2.5 design on there without issue. That's on the single head or the multi-head. Singles, particularly your desktop variety are closer or at 2" in height (regardless if it's low, mid, or high profile). That extra half inch allows for a lot, designs that wouldn't normally be able to translate as well, that helps them a great deal.
Now, digitizing is a whole other can of worms. Rather you plan on doing it yourself or outsourcing that part of it, I would suggest you get Wilcom software. Again, not one of the cheapest, but it is the best. Unlike the immortal Ai v Corel and/or PC v MAC debates, there are significant differences in these software packages, even if you digitize correctly and that is what is called the stitch engine (the algorithm that generates the stitches after you digitize objects). That and the sheer functionality of Wilcom (especially if you use the full version) just blows the others away.
Attached is the type of single head that I would suggest. That is our specialty embroidery machine (it does regular embroidery, as well as, sequin embroidery), so don't need to worry about that part of it, just the fact that it is a bridge style. It has all the functionality of your multi-heads, just compressed into a single head.
Now, one word of caution with your multi-heads, especially 3 heads on up. Stay away from the step motor driven machines. There is a particular quirk with those machines with 3 or more heads. The further away from the motor you are, the sloppier the pantograph can get, typically on hats due to their special digitizing needs. Your first two heads, no problem. Third head maybe/maybe not. That fourth head on, more than likely heading for the trash bin. Go servo driven. For your single head, it doesn't matter, but your multi-heads past two heads, it does. You can mitigate that with even more special digitizing, if the digitizer is aware of the issue, more frequent servicing of the machine etc. Just be aware of the quirk with your step motor machines.
This is it in a nut shell, if you have any other questions, concerns, comments just let me know here on in the email in my signature. Hope this was helpful.