My blender looks to be on it's last legs (it's started slipping and smoking!)

Can anyone suggest what one piece of kitchen kit would be most suitable to buy for LC/Paleo baking?

Just to add, I'm looking to do a range of functions - grind nuts, puree fruit and veg, and hopefully also whisk/whip eggs

I haven't tried it, but the magic bullet looks to be good. Get something small and easy to put together and clean. I have a great food processor/blender combo that almost never gets used. Pulling it out, setting in the right disks and then cleaning the whole thing after is often more trouble then I want to go through.

A lot is going to depend on how much you want to spend. I know many people love the VitaMix, but I can't afford to spend $500 for a kitchen appliance. I have an Oster blender with a small Chopper attachment that I like very well. I also have a large food processor, and intend to buy a small food processor. They all serve different purposes, and each performs certain tasks better than the others do. I'm not sure the VitaMix, even as expensive as it is, could replace all 3 appliances perfectly.

ETA: Then there is the KitchenAid stand mixer to consider. It certainly is versatile, if you buy all the attachments, but you're getting into quite a bit of money there, too.

Well... a food processor can whip cream but a stand mixer can't chop nuts.

I have both, like having two appliances!

I'm beginning to realise I'm probably going to have to just buy another blender and then something else to whip stuff. The Magic Bullet says it can do both but it seems so complicated.

A stick blender... that might be a good option for you. They usually come with an attachment you can grind things in.