The width of your border is dependent on the size of your garden generally, and also what kind of plants you want in the border. Even small shrubs will require a minimum of 3 feet depth from front to back, and for a layered effect, it's better to have a border that's 4 or 5 feet deep, even if thats only in parts because its curved in and out. If you just want to grow, say, annuals, or summer bedding, then you can have a narrow border.
If the soil is heavy clay, you'd be best off buying as much composted material as you can get hold of rather than woodchips, dig it in, level off with a rake, plant up after a week or so, then you can add woodchips to the surface to keep moisture in and weeds down if you want. the woodchips will break down over time and benefit the soil over a couple of years.

i would plant your seedlings in cell trays so you get strong plants before planting out.
Changing heavy clay soils takes a long time. There is no alternative to good old double digging in the autumn,adding manure/compost, and then a good dig in the spring.

You could also dig in some coarse grit which helps to break up the clay. Scrumpygrat's right - it takes some years to really see a significant improvement. Just add all the humus containing materiaL you can - old compost from pots and tubs etc, composted kitchen and garden waste etc. If you get dead leaves in the autumn put them on the lawn and mow them and then heap them up to rot - the rot more quickly cut up (ie in one year rather than two) You can go on mulching like this for years and the soil will get better all the time. Even lawn mowings make a good soil conditioner if left to rot for several years.

Incidentally you don't lay a mulch first and then plant, its the other way about. Hows about if you have mainly fairly easy to grow annuals this year, and save putting in any shrubs and perennials until the autumn? Don't put small seedlings straight into a heavy clay soil - wait until they get bigger. Only use the bark as a mulch rather than a soil conditioner - but I wouldn't use it at all, because any mulching with compost will just cover it up.

Roses love a clay soil.

Thanks for all your comments!