WiFi network design advice needed

I am in the planning stages of replacing a mish-mash of WiFi routers for a new client, and I've never had to design something this complicated.  I'm mostly a programmer, and definitely NOT a networking (much less WiFi) guru.

What they currently have is a set of low-end consumer routers - mostly Linksys (or worse) junk - spread out through 4 buildings on about a 4-acre campus.

Currently, all the routers are hardwired back to a server room, where there is a Peplink Balance210 router/firewall in between the LAN and WAN.  All the WiFi routers are in whatever version of access point mode they support - for most that's nothing more than turning off their DHCP servers.

I have two major problems to solve here.  First,, the client wants to have a internet-access-only guest network throughout the campus, while simultaneously giving privileged users access to the LAN.  Only a couple of the existing routers (Asus RT-AC68P) even have support for a guest network, but since they aren't directly tied into the WAN, the "guest" network still sees the local LAN.  And none of the other routers in the remaining buildings have ANY guest network support, or even any support for multilple SSIDs at all.

Second issue is that none of these routers support more than a couple dozen simultaneous WiFi clients.  The client is a medium-sized church (500+ seats in the sanctuary), and they want to be able to have 100+ WiFi connections going just in the sanctuary.

I need a solution that will solve both above issues, while:

1. Hopefully re-using at least the "good" Asus routers,

2. and remaining as inexpensive as possible.  I've got a budget of about $1,000 - much more than that and they'll just scrap the whole idea.

I've looked at the Open-Mesh product line, and I think they would do what I need, within or at least close to the budget,  but I'd rather use Netgear.  It's all I use personally and for more basic WiFi setups for clients.  However, when I looked at the "business-level" Netgear stuff, it seems definitely out of my budget.

Thanks for reading this far, and I'm open to all suggestions.