I don't think there's a good tutorial on patches here, but you'll probably find
this site really useful. In general though, I'd look around for an online tutorial on subtractive synthesis; it's the mechanism that workstation keyboards tend to use to produce sound. The main difference is that instead of using one of a few simple waveforms, like old analog synths would do, workstations will use a more complex sampled waveform instead. I'd suggest learning the basics of subtractive synthesis, at least conceptually, before diving into the Motif, at least if you want to make your own patches from scratch.
As for getting better sound out of the Motif, you certainly could do things from scratch, but you'd probably be better served taking existing patches as a starting point and tweaking them. It'd save you a lot of time and be a good learning opportunity - seeing how Yamaha made the preset instead of starting fresh and trying to get to the same point.
Knowing that you *have* to spend money makes things different. I would agree that a Yamaha probably makes sense because, as you said, it'll have a common interface. You might not be able to share patches directly between the Motif and something else, but you'd at least be able to recreate them easily.
The s90 is based on the Motif ES, not the XS, and I don't believe it has the full set of samples that the Motif ES has. In fact, I just looked it up and the s90 has *more*, although that may just be because it's a cross between a workstation and a digital piano so they may be using a lot of samples to get the perfect piano sound. It may be that the Motif ES still has more variety.
I have two suggestions for you. One is, if at all possible, to avoid using the s90 in the rehearsal space and use your own gear. The only way using the s90 would be a good idea is if you end up with an s90 and are saving presets on a USB stick and copying them to the other s90. I play at church frequently too, and my method is to figure out sounds for a service on my own at home before rehearsal (which for us is sadly just on Sunday right before the service; we could use a mid-week rehearsal too). At rehearsal, I make small adjustments based on what the other musicians are doing. The key is that I'll save the presets so that I don't have to remember things during the service. I tend not to tweak individual patches, but I use combi mode exclusively (somewhat equivalent to master mode on Yamahas, i think) to make pads and other sounds made up of multiple patches and to get the right behaviour for MIDI (I use both my keyboards whenever I play). I'll often tweak the volumes of parts within a combi or change drawbars on my Nord Stage during rehearsal and want to capture that so I play it the same way during the service.
In your case, if you have a keyboard player who's going to be playing the Motif on Sunday, they should rehearse on the Motif so you know they're getting the same sounds. If they're savvy, they'll reorganize presets so they're in a logical order for the service, letting them do something like hit 'next' to move from one song to the next, instead of having to write down that they need preset #109 in bank B and punch that in.
As for keyboards, I agree that the s90 is a good choice. Really, your only other options within Yamaha would be the M08, which will be well under budget (could you use the rest for good keyboard stands, benches, etc?) or a second Motif-class keyboard. A new Motif XS will be out of your price range ($2,400 for a 61-key on sweetwater.com) and the ES and regular Motif aren't in stores anymore, but you might be able to find one used? It would probably be ideal for your keyboard players if they could use the same keyboard no matter which location they were playing at.
Good luck!