I’ll check the Wikipedia info. We have a v.4.0, so that shouldn’t be too much of a problem.

Oh yeah, Wikipedia has information, including a good table of the specs of the various hardware revisions, and of course, lots more links to get into.
All Linux, except for the WRT54G v5.0.
The latest GS has only 4 Mb of Flash, but that should be fine, since I’m using the G model, which only ever had 4 Mb. Some folks liked the added space in the GS.
Usually the hardware revision is on the model/serial sticker on the bottom of the unit.

First, before upgrading anything, confirm again the model (WRT-54G or WRT-54GS) as well as the version.
I started off with Sveasoft‘s “Alchemy” firmware and upgraded about a month ago to the “Talisman” firmware (basic featureset). I’m pretty happy with it, but as Rusty has already pointed out, there’s the caveat of the yearly subscription fee and a hotly contested business model. It’s also a pretty geeky firmware that adds in things like VLAN tagging and QoS features, which are probably not anything you’ll ever need to worry about.
DD-WRT is an offshoot from the Alchemy firmware and seems to be popular.
HyperWRT is another popular one that I’m aware of and boasts both stability and ease of installation.
My adviuce is to AVOID OpenWRT if anybody pitches it to you becase it’s a compile-from-scratch DIY Linuxgeekstravaganza and is way more hassle than you’re looking for.

On the transmit power
Check around before you change it and be careful. I’ve heard reports you can fry the radio chip by setting the power to the max.
Changing the transmit power won’t do anything to help the receive sensitivity, but the longer antennas will. Remember, it’s two-way, if the router can’t hear your laptop, that doesn’t work either.

Wow, welcome to the Linksys Router Club and the Canon Powershot A620 club (that’s the camera I just got too).
I’m using Sveasoft’s Alchemy software (which was current when I installed it a year or more ago), but they want their $20 a year, and there is a lot of debate over whether they’re handling the GNU business correctly.
It’s working so I won’t touch it, but if I wanted to try another one, I’d use HyperWRT, because like Sveasoft, it keeps the original Linksys web interface and only modifies it.
Some of the firmware can only be configured by command line. I don’t think you want that.
Also, there are long dipoles available for those models, which will help with the effective range. Another thing that helps is getting away from Channel 6, which is the default and likely to be the one in use by everybody else nearby. Use channel 1 or 11 (1, 6, and 11 are actually the only non-overlapping channels).

I’ll be damned. That’s a whole approach I hadn’t even thought of. And it looks like there’s quite a variety to choose from. Any thoughts on which to pursue? (If not, I can slog through their forums, it looks like)