Are there *recommended* alternatives to using the problematic Broadcom 43** chipsets?

Intel chipsets are usually well supported. I think Atheros are as well, though I have no experience with them. One place to do a little research is the Linux Wireless site as they are the ones writing the drivers.

I've always used the Intels. Never had issues as long as I remembered to load the firmware. Most of them have pretty good performance too.

Next question, (as I have zero experience in laptops save for replacing a hard drive or two):
Is this something that 1) can be obtained readily & at a reasonable price, and 2) can be easily replaced?

1) Usually wireless cards aren't that expensive. The hardest bit will probably be doing your homework on which makers use which chipsets. One of the frustrating things about wireless cards is that the manufacturers frequently use whatever chipset is cheap that week, and may not bother to change the model number of the card.

2)Since this is a laptop, then there is a good chance the thing is soldered to the motherboard. In that case, you'll probably need to look for a USB based wireless card. Again, you're going to want to do some research in to the specific brands/models as USB wireless sticks can present their own unique challenges. Even if it isn't soldered to the motherboard, you'll have to look at the form factor it uses. That will probably cut down on your options significantly.