My personal preference is a basket, but definitely get either panniers or a basket. My spouse developed some pretty bad neck pain due to commuting with a heavy laptop in a backpack every day. Some other ideas:
1. Instead of transporting a laptop, could you just carry a small USB hard drive with your files on it? Or use the cloud? I realize specialized software, or workplace IT policies, can frustrate these plans. Laptop avoidance should be at the top of the list for bike commuters.
2. Make sure you're equipped with the means to fix a flat while on the road. Otherwise it will happen
exactly at the 6.5 mile mark, in the rain.
3. I don't think there's much you can do about a too-tall bike except get a new bike. Being too tall may also mean that the bike is too long. Don't go back to the same shop.
4. My own approach is not to work through pain. You might be better off in the long run, riding every other day, until you get all of the kinks, aches, and pains worked out. A few more car rides won't be a big deal in the grand scheme of things if it helps you make biking a more regular part of your life.
5. Every cyclist comes from a different place in terms of their mechanical skills and experience. If you've depended on a shop to take care of minor repairs, this is a good time to start heading up the learning curve on maintenance.