HELLO & WELCOME
If you like the stock launcher, you could either run Steel Droid or actually just root the stock ROM and use an app freezer like Titanium Backup Free to freeze some troublesome stock apps that start unbidden. I use the stock ROM rooted and have just a few things frozen, like the stock IM client, Social Location or whatever, things like that that auto start without me launching them. Be sort of careful what you freeze and you won't have big problems, also try to freeze one app at a time and run that way for a day or so to make sure you don't get crashes.
That said, the stock ROM DOES have a known issue with rebooting. The phone doesn't actually power off, it's more like a system software restart (like you used to be able to restart Windows 98 by holding Ctrl without power cycling). If this bugs you and you don't want to hear "DROID" from your phone in your pocket in a business meeting you'd be better off running any other custom ROM.
I ran Maverick for a while and there were several things I liked about it, but I can't remember why I switched back to stock at the moment. I do really like the stock launcher, and with problem apps frozen it runs just fine for me, so it hasn't bothered me enough to make me switch. Apps eating up the smaller RAM were my main problem with the stock ROM.
I used to run Steel Droid when I first started trying custom ROMs, but it has some really weird customization somewhere that screws up all the button graphics in Market (Play Store now). It pissed me off enough that I switched off of it, YMMV. Other than that I can't remember any performance issues under SD, it may have been a bit harder on the battery, but on this phone you'll be fighting that battle all the time anyway.
I use the car dock a LOT and love it. The Droid 3 has a bit of custom software where it has a separate Car Home launcher thing that is cool; if you hit Navigation while it's up, it displays a constantly updated map with your location centered, your speed and compass heading, and quicklaunch buttons on the side that are shortcuts to Maps and Navigation. <3. It reminds me of the experience you get when you have a dedicated GPS unit on your dash and have it turned on, but not routing you to a destination, just sort of following you along and giving you information. I use it more and more every day, usually for things like trying to see when a turn is coming up without running full Navigation, if I sort of know where I'm going, if I can't listen to the voice prompts for some reason, "did I pass that turn already?", SO MANY USES. Also neat is the fact that it pulls down map data from Google Maps, so it's realtime, always updated, etc, and thus better than a standalone GPS. If you want to search nearby for Places or something, you can always jump into full Maps with the quicklaunch button, too. LOVE LOVE LOVE.
If you do get one, esp. from Verizon like I did, maybe ask them about getting the original cable with it; they originally came packaged with a single cable that hooks into the dock's micro USB port that split off into a full size USB plug on one cord and a line out 3.5mm (headphone) plug on the other, that would be so handy just for better cable management. I didn't get it with mine, and use the separate car charger (without a USB port on it) and line out cord, just sort of wish I could have that other cable.
I second darthakakios's recommendation for an extended battery. You can get a few 3500mA batteries with a crazy-thick battery cover online, but if you want/use any docks you'll probably have to stick with the official extended battery & back. It's not extended by much at all, goes from like 1500mA stock to 1750 or something but I'm sure that little bit helps. As it is, I pretty much charge mine whenever I can through the day, esp. in the car. I'm a pretty heavy user, though, and I have either Play Music or Google Listen running for most of the day, web browse & download sort of heavy, use it to read PDF manuals onsite, etc.