Is there anything you could especially recommend for this job? (I'm not afraid of getting my hands dirty, BTW :oD)
+1 for Linksys WRT54GL and tomato firmware +1 for pfsense (or monowall) on a small server
The Linksys is going to be your cheapest option and will take the least amount of time to setup. It is also the least featureful. As far as support goes, just buy a spare and keep it around in case something goes wrong with the primary unit. In my experience, I've never had to reboot a Linksys running tomato. However, I have had bad power adapters or routers die in the past, so I would keep a spare for any application that required mid level availability.
pfsense (a fork of monowall) is great on any device I've tried it on. And it should offer basic DNS and NTP serving ability that the Linksys may lack. Your performance/availability is going to be limited by your hardware here as well. If you need high availability, I'd recommend a name brand Dell/HP/etc with a warranty and redundant hardware. If some downtime is acceptable to the the client, then perhaps forgo the redundancy but keep the warranty or get a spare box.
The great thing about the Linksys is that it will likely pay for itself inside of a year due to the lower operating costs and low initial investment. A server based box may not pay for itself, but could provide additional features (enhanced security, VPN, authenticated wifi hotspot, etc) that would be worthwhile to the client.