clematis Montana Elizabeth,in no time you ll have a lovely covering.
Non-variegated ivies grow faster than variegated ones. Ivy takes a year or so to develop a good root system then takes off, IME. It is then hard to get rid of! There are some evergreen clematis, of course, such as armandii, as well as evergreen honeysuckle. Clematis armandii grows fast but is not always hardy. Obviously, that kind of thing needs support. I have read that persian ivy (hedera colchica) is fast growing, but haven't grown it.
Not sure about Ivy but Clemantis cirrhosa - jingle bells is an evergreen, can't remember the name of the other one which I grow, non invasive but has rigorous growth. Flowers at Christmas time or shortly afterwards.
Ivy will cover your shed - unless you trim it very regularly and keep it under control it will also get under the eaves and force it's way between the walls and the roof making both unstable - it will suck the moisture from any foundations causing them to crumble. The only thing likely to do more damage is Russian Vine
Just bear in mind that winter flowering clematis are not quite as hardy as summer flowering ones, which are generally very tough. They need wires or trellis to support them because they are not self-clinging.
I've got Clematis cirrhosa Freckles but I wouldn't call it fast-growing. Had it about 5 years now and it's about 2m tall, up an obelisk. It does indeed flower throughout winter though.