Router IP (Best Practice)

There isn't a rule that says explicitly "use the last IP on the subnet for the router".

You might as well use the middle one, but one thing that needs to be true is consistency. Its easier to remember the default gateway if you use one consistent way to assign them.

Further, assigning them either at the end or at the beginning makes it administratively easier to assign DHCP ranges etc.

This is merely preferential. Most people prefer to use the .1 or .254 in a simple classed subnet.

I'm fairly sure that it's for the sake of convenience.

It doesn't, really, matter what you pick as your "router IP". Just make sure you're consistent. I, personally, prefer "lowest host IP for default gateway" (with physical IPs for routers participating in HSRP being the next few up). But "highest possible host IP for default gateway" is equally good (you'd then presumably pick the next few lower IPs as the physical IPs for HSRP interfaces, to the extent you use HSRP).

However, having "highest" on some LANs, "lowest" on some and router IPs half-way through the raneg on one or two will cause issues, down the line.