At the end of the day, it's not so much the material you use, it's how you use it. Everything bends and flexes. For a machine of any construction to work well, it has to be designed to resist bending and flexing. I hate working with steel. If you don't mind it, it's definitely cheaper to weld up a massively strong and solid frame. But it's no free lunch, as most likely your bearing surfaces won't be flat, which brings about a lot of other issues. I have equipment at my disposal which allows me to easily get perfectly flat surfaces from wood, so that's the route I take. Aluminum extrusions are expensive, but easiest to work with for most people. But I'm not sure if there as rigid as some people would lead you to believe. Or rather a lot of people use smaller sizes than they should, in the interest of cost savings.

I say build with whatever material you like, but you need to know how to use each material properly, and to it's strengths.

Also, with regards to linear bearings. Take a good hard look at what the total machine cost will end up being, and in a lot of cases you'll find that upgrading the linear bearings may only end up being not more than £500 more, which is well worth it in the long run.