Not the cheapest option, but I bought a CX bike for commuting and have been delighted with the flexibility it offers. It isn't as quick as I expected with the CX tyres but if you want the extra speed you can always put some slicks on it and it's pretty nippy. Also handy for hitting a few fireroads and offroad sections to lengthen the commute in the summer months, added bonus you can race it in the winter too.
EDIT: And I use it plenty on the turbo trainer too! Buy a cheap rim and turbo tyre and just flip it over when you want to ride the turbo.