Building Custom Speakers?

tube amps are superior to solid state amps, am I right?

Massive question with no real answer - yes in some situations/applications, no in others, and very dependent on the amp design.

Of course you can build them and many do, if you take on that and a speaker project you may as well cancel "life". But if you want to get into DIY I would say an amp project is probably a better start than a speaker. Less farting around with wood, easier to understand the critical stuff and more likely to get a good result. But do you have money to spend?? You'll need to buy a kit or good components.

http://www.hificollective.co.uk/index.html
http://www.diyaudio.com/forums/solid-state/
http://www.diyaudio.com/forums/tubes-valves/

Or search amp + kit in ebay for loads and loads of chinese stuff - some of which is reckoned to be decent these days.

Are Crossovers expensive to get right?

Time consuming mainly, also require fairly high level of understanding of your speaker design, and tend to need a bit of real-life testing to dial them in, but also not cheap when you start looking as decent components.

And I was thinking of trying to replicate/improve one that BBC speaker in the first post and adding a bass driver.

Not a bad aspiration but the LS3/5 has a complicated cabinet design.

Fundamental fact - if you are putting together a system on a budget you are likely to get better results/return by carefully sourcing good second hand gear than building your own. Don't beleive me? Try building me a better sounding speaker than these for the money:

http://cgi.ebay.co.uk/Kef-Q35-/180638053831?pt=UK_AudioVideoElectronics_HomeAudioHiFi_HiFiSpeakers&hash=item2a0eddf5c7

http://cgi.ebay.co.uk/Mission-782-Main-Stereo-Speakers-/320666747145?pt=UK_AudioVideoElectronics_HomeAudioHiFi_HiFiSpeakers&hash=item4aa93a4109

http://cgi.ebay.co.uk/TANNOY-611-MkII-DUAL-CONCENTRIC-BI-WIRABLE-SPEAKERS-/230598406609?pt=UK_AudioVideoElectronics_HomeAudioHiFi_HiFiSpeakers&hash=item35b0bc71d1

Same goes for amps etc.