I don't know if it's the one for you, really, but I use OpenRPG. It's free, easy to learn (the basics anyway, you'd have to ask around the forum or the OpenRPG Dev II server to learn all the other options and uses, plus there are utilities and such you can find on the web since OpenRPG is open content for other developers), it has a map and an easy way to store and transfer character sheets/other data in the .xml file "nodes", and it has a decent number of gamers that've been using it for many years and gets new gamers all the time. You can save your chat-buffer as a session log for later review (or to send to folks who missed a session, since the chat-log is an .htm or .html file), and I think the current version of OpenRPG might automatically do that, but I'm not sure where it does so (I just know that it auto-saves some kind of log nowadays).
Now, while the map has an adjustable/optional grid and can display images you have stored elsewhere online (usually on PhotoBucket or a personal webpage or something of the sort), and can display images of miniatures that can be moved around the map, it does have some minor issues. I'm not sure if the fog of war is working reliably in the current version (I think it is, or at least I've seen it used in one game I played in), and the map can slow things down if you or others on the server don't have reasonably fast computers, but it hasn't caused me too many problems when DMing (and mine are generally because my own computer is old and slow). Also, I think miniatures have to be .jpg images, though one or two other types might work (.gif images either stall the program for a few minutes, or otherwise cause trouble, and won't display). Minis have to be images that are also stored online somewhere. You can draw on the map as well.
On OpenRPG, you can visit any of the servers online at the moment or run your own temporary server on your computer, easily enough (that's what I used to do, though lately I just host my games on the Dev II server). In each server, there's a lobby and people can create separate rooms for their games (the lobby isn't generally for gaming, just chatting). The rooms can be made private or open, with private ones using a password for entry.
Minor note: the only serious problem with OpenRPG is that, once in a while, something your computer does just might freeze up OpenRPG or corrupt its current Gametree file, forcing you to stop the program and possibly reset the computer (at least in my cases, because again, my machine is old and runs a cruddy version of Windows). This happens only rarely (in my 7 or 8 years using the program, I could count the number of times on one hand and still have fingers left, but it's been so rare that I can't even remember exactly how few times it's happened). I've only seen or heard a few other people having this problem.
This is easily compensated for by just saving a separate copy of your Gametree under a different filename, or better, saving your individual nodes separately from the Gametree. Whenever you finish a session and changed some nodes during that time, just save the changed nodes or the spare gametree file before closing out. The program automatically saves your gametree when closing out, but on the rare occasions where the gametree file gets corrupted in the process, or when the program freezes up from some background-program of your OS interfering once in a while (as it does on my machine, anyway), this auto-save won't help as a result of the corruption or freezing.
Other minor problem: Once in a blue moon, the OpenRPG website will be down for maintenance, and OpenRPG will not be able to start up properly during that time. This has only interfered with my games twice now.
) someone else can step into their shoes to keep the application up to date.
)
