I don't usually jump into these sorts of debates, but I have a little background that might help. I work in public safety communications, and also spent several years helping set up and running a large church-based comm system utilizing 5 simplex UHF frequencies, about 50 portables, and a communications center for our summer bible camp which drew about 5000 people including children and adult staffers. Here's my two cents worth...
The only thing that I think is undesirable about these things is the dual PTT button, and of course, the mediocre build quality. But they are a big step-up from the bubble pack radios we were using for a while.
We were looking for about a dozen. Like I've been saying, I have a $1000 budget as it stands right now. I may be able to squeeze an extra hundred or two into that, but not much more. Its sad really, but with a $1000 a year budget, if one ore two break once in a blue moon, the $50 to replace it would not be that big of a deal. It would also not be a problem if we decided to make it a "you break it, you bought it" policy.
If you already notice the 'mediocre build quality', then that should be a red flag for you right there. I haven't personally played with any of the recent Chinese 'disposable' radios, but what I have heard about them has not impressed me. Being familiar with what you are trying to do, and likely how you will be using the radios (I would take our comms 'on the road' throughout the year when we would take groups to Christian camps for outings), I think you will discover that it will be more expensive in the long run to buy all your Baofengs (or whatever you choose) up front and then deal with repair and replacement as they get broken, than it would to do as someone else mentioned and get quality radios (I like the Moto CP200's, but any business-quality radio brand will work) even if you have to buy them in stages. Yes, they may be cheaper to replace, but I will almost guarantee you that a dropped Baofeng will be more likely to stop working than a dropped CP200. We use the 200's and they get abused, usually by people who only know how to turn them on, and not much else. They fall from belts, get carried by the antenna, get left lying around, etc, etc, etc. They are robust, and we seldom had to replace them. There is more to overall cost of service than just the initial purchase price.
You can go though a shop and buy them new (or possibly second-hand if they have any that have been traded by someone else), and they will handle your programming and set-up for you (for a price).
If, and ONLY IF, you have someone in your organization who is radio-savvy, or wants to learn to be, you can try another option: Research and buy your radios on the open market (*Bay, etc), contact Motorola (or whoever the maker is), purchase a copy of the programming software, and you can set up and manage your own system. This route is not for someone with no radio knowledge or skill, but it also is not rocket science if you are computer literate, and somewhat technically capable. The key here is to stay legal doing it, and ask questions if you don't understand something. I have never had a problem finding radio professionals who were willing to help me out with technical questions, especially since you ARE a non-profit and not making money off the radios.
Frequency bands: Our church system is on UHF, and it worked for us at first. But as our footprint expanded, I really wished we were on VHF, because we began having trouble talking from one end of the campus to the other (there were some large buildings and terrain features in the middle). We did not have a repeater, and although I tried for several years to get them to install one, senior staff felt it was not financially feasible, even though everyone agreed we had outgrown our current system. Generally speaking, UHF propagates better in buildings and urban areas, while VHF has better range in the open. Having two radios side by side (UHF 4 watt and VHF 5 watt) in an open environment, you will usually find that VHF carries farther than UHF, dependent upon certain variables. I work almost exclusively with VHF in my job, and UHF in my church gig, so I have a lot of experience with both. I would strongly recommend you listen to the other people here who have recommended VHF for your application. Picking a radio and then tailoring your system around it is usually the backwards way to engineer a system. You should pick the frequency band that best suits your operation, get the frequencies licensed, THEN choose the best radio to meet your requirements.
There is a lot of great knowledge on here, and most people want to help, but bear in mind that each of us have our own opinions on what is 'best'. If in doubt, always consult someone locally (radio shop, techs, comm person for another local organization) who knows your specific variables.
Good luck!!