You definitely need to be using DI boxes on the acoustic guitars, preferably "active" types. Simply changing the physical connector from 1/4" to an XLR will not help you. The active DI will convert the relatively low output from the acoustic guitar's pick-up/preamp to a higher ("hotter") output level. And even more importantly,it will convert the unbalanced output to a balanced one, so that it is more immune to picking up RF-induced noise when going down the snake. By the way, this is may be why you're getting the noise you are asking about in the Live Sound section...
The guitar that you are experiencing "thin" tone with in all likelihood is either equipped with no onboard preamp, or an inferior one. And the bass guitar-please tell me that you are plugging that into a dedicated bass amp, not just the PA system. The reason that I say that is because :
A) Bass guitar can do serious damage to the lightweight speakers in a lot of the cheaper PA cabinets out there,
B) It will "rob" the clarity of the vocals in small systems like yours,
C) Using a suitable amp onstage will give the band the "feel" that they need to generate a "musical" performance. Especially if you end up having a drummer onstage, but even if you don't.
D)Even though you want to try to keep the bass out of the PA system, most modern bass amps provide a DI output to facilitate their connection to the PA if needed. So you can get away with using a smaller amp with a DI output hooked to the PA, but not mixed into the monitors, which will help prevent some of the above issues.
Now, which DI boxes to get? For the acoustic guitars you should definitely get "active" models. These have little opamp circuits in them that will boost the output and balance the signal. Countryman and Radial make the better ones out there, but these aren't cheap. In the States, about 180 dollars. The Radials are made in Canada, Countryman in the US. A couple of less expensive, but still decent quality brands are ProCo and Whirlwind, at about half the price. And lately, I've been using BSS DI boxes I've bought off of e-Bay for about $90 each. These are good for acoustic-electric guitars. Try to stay away from the cheap crappy boxes from Behr&^&^%r, Tapco,Rolls, etc. These don't filter RF noise well, plus the cheap build quality makes them unreliable, especially if you're having to plug/unplug them every Sunday.
If you're stuck having to DI the bass with no bass amp, you can use one of these active boxes, too. If you do have a bass amp, but it has no DI output, you can get by with a "passive" DI box. These have a transformer in them instead of an opamp circuit. Transformers have the advantage of being more immune to RF noises, but their downside is that they tend to lower the output level of the source to the mixer. Both ProCo and Whirlwind offer great passive boxes at a good price, as does Radial (but they're more $$). In any case, make sure that the DI boxes you buy have a GROUND LIFT switch! All of the brands I listed do, but there are some cheaper "knock-offs" that don't so beware!

Thanks for your patience in the reply. Unfortunately, I just know how to work the equipment and I'm trying to improve things. I know very little about creating proper setups.
That's something else to add to the long list of things learned from this site: guitars need DI boxes.

Fortunately, the band doesn't play every Sunday, maybe 2-3 times in 3 months. The worst is when we need to hike all the equipment from church A to church B, set up and play an hour gig, then move it all back, generally by tossing it all into someone's car boot.

The note about RF noise explains a lot. The guitars do buzz a little more than the mikes, for instance.
Note to self: pester minister for funding for mikes/DI boxes. Maybe a powered monitor, and some assorted XLRs.

Say I used something like [[url=http://[/URL]="http://www.bosscorp…"]this[/]="http://www.bosscorp…"]this[/] I assume it would do the job, but I would need to activate the phantom power on the mixer?

The only spec they list is "current draw", but i would think that it would run off of phantom power. A BIG caveat here: check with Roland first, do not assume anything with them! In addition, Roland has earned a HORRIBLE reputation with their live sound products over the years. They do not hold up very well, Roland "dumps" the products after a limited run, and they are usually not cost-effective. I would strongly recommend looking elsewhere.

Oh right. I just did a quick search for DI boxes to see roughly what we'd need.
It mentioned phantom power on the overview page, saying that it'll run off batteries/phantom power.

We'll definitely do some searching before getting any though, I can't say I've seen any shops that sell DI boxes around here, so we'll need to get them online, which ought to take time.