As others have said, no specialist clothing is really needed.

As for the bike, the general rule for those on a budget, is that an older inexpensive used bike will be much higher quality than a new bike of comparable price.

Assuming you are in England, I'm tempted to point you to the old Raleigh 3-speed "English Racer" types. They ought to be plentiful in Britain, and are great commuters. But then again, there are lots of older bikes that would be fantastic, so no need to limit yourself to one type.

I hope you are ok.