Amazon sells them for decent prices at this point. I'd recommend the Motorola extended battery, which is a little bigger than the stock battery. It does require a new back, as it is a mm or so thicker than the stock battery, but it will still fit in the Droid 3 car mount, and you'll barely notice the difference. It should give about 20% more battery life.
Amazon does have it here for $40 at the moment:
Amazon.com: Motorola Droid 3 Oem Extended Battery Bf6x and Cover Door: Cell Phones & Accessories
But you can also buy the two parts separately for $12 and $13.50:
Amazon.com: Motorola Droid 3 Extended Battery (BF6X) Motorola XT862 Droid 3: Cell Phones & Accessories
Amazon.com: Motorola Brand New OEM Extended Battery Door Moto XT862/DROID 3 - Battery - Bulk Packaging - Black: Cell Phones & Accessories
If you want just a normal battery, those are really cheap:
Amazon.com: Motorola BF5X Bravo Defy MB520 Battery SNN5877A: Cell Phones & Accessories
While you may find some third party brand batteries that say that they work with the Droid 3, I really recommend sticking with Motorola batteries. The third party batteries do not always live up to their stated capacities, but Motorola batteries always work well.
To remove bloatware, you need to root the phone, but I think that bloatware as a cause of slowness is overrated. Don't run the bloatware, and it won't slow down the phone. We have an All Things Root forum here to discuss issues around rooting.
I think that the Motorola home screen causes a lot of problems with the phone, especially as it runs for a long time, so you may want to try restarting the phone every day or so. If you charge it every night while you sleep, shut the phone down and restart it when you get ready to plug it in to charge while you sleep.
What do you mean by a larger keyboard? Do you mean a software, on screen keyboard with larger letters, or do you mean a Bluetooth hardware keyboard of some sort?
