How fast do you want the VPN to be? What technology are you using, OpenVPN, WireGuard, something else?
What is driving you to put the conflicting goals of security (VPN, firewall) with file sharing and a web server on the same box, one that is directly exposed to the Internet?
With no budget, you should have at least two or three devices (firewall, VPN, containerized web and file sharing), a managed switch, and a wireless AP.. None except the last are an all-in-one router.
(Edit: Marvell wireless drivers don't support 802.11s mesh, at least last I checked. Three-radio devices have advantages for mesh when wanting more than about 1/3 of the channel bandwidth.)
VPN: is for private use, it doesn't have to be that fast (no streaming for example).
"Conflicting goals": I try to avoid several devices that use energy. For sensitive data I use my personal nextcloud on webspace. If I could put music/video on the webstorage of the router I'd be happy.
I guess for a good router 80-150$ should be enough.
On the other hand I pay for webspace every month some $. I'd even pay for the service, that someone establishs and maybe even sometimes maintains my NAS with email, nextcloud, wordpress, phpbb. But I think I keep that better on the webspace which is not much work, not that expensive and even more reliable than at home.
“Mesh” only is meaningful for three or more APs where you have more than one path. With two, point-to-point, such as WDS, is sufficient. I run Linksys EA8300 units in a mesh. I chose them as they have three radios so that I don’t lose bandwidth to the backhaul and that they run a current, multi-core, ARM-based processor. If you don’t need wireless backhaul, the similar EA6350(v3) is a more economical choice. There are other ipq40xx-based all-in-ones as well. The ipq806x and mvebu devices tend to be over US$100 .
Running your servers on another host, VPS or managed, or locally seems wise to me for many reasons. An x86_64/AMD64 iTX or SBC with two, mirrored Samsung or Corsair SSDs (ZFS) can idle under 10 W at the wall. use APU2C4 and APU3C4 units, and will probably switch to the more current ODRIOD H2.
High-end routers can consume more than 10 W. There is no “magic” - more processing speed, more power consumption.
Just found an old Netgear WNDR4000. There is a stable openwrt 18.06.4 available. Does that mean that a mesh is possible with all routers with this openwrt version? I have several old routers around.
With current OpenWrt, 802.11s i supported by most Qualcomm/Atheros wireless radios. Some of the older units require the "mainline" or non-CT drivers and firmware. IBSS support is also generally good.
Once you have a suitable device, I would consider flashing 19.07 (snapshot right now, but I have read it contains LuCI) as 18.06 is "old".