It can be difficult to source well-made clothes that fit over cloth nappies, as most clothes are cut for disposables. You may find that you need clothes at least one size bigger if they do up under the crotch, or go round baby's bottom. Also, you will find that trousers may well drag your nappy wrap down, because of insufficient crotch depth. This is more of an issue with a newborn baby than an older child, as the ratio of baby to nappy is quite small!
The problem with sizing up in vests a little early is that you'll then find the shoulders are too big. In this case, you may like to consider getting a pack of vest extenders. These are a handy little rectangle of cotton which snaps onto a vest to lengthen the crotch.
If your budget stretches to it, you could buy clothes especially cut for cloth nappies. American high street clothing brands tend to have many more clothes cut for cloth nappies, and prices will be very competitive; equally Scandinavian brands tend to have a more generous cut too. In the UK, we would recommend Frugi.
If you find it difficult to source specific cloth nappy-friendly clothing brands, there are still plenty of widely available UK brands that you can make work with your nappies. In our experience, vests from supermarket brands or M&S tend to be more generous in the 'right' age range to fit over cloth nappies without compromising on the overall fit. Another recommendation from one of our customers was the LOGG clothing range in H&M. They tend to be wider and fit over cloth nappies easily and are also very inexpensive.
The type of clothing you choose can also make a difference: leggings or tights can be a bit snug over a bulky cloth nappy so may lead to compression leaks with a microfibre nappy (not to mention stretching the clothes!). You might instead consider looser jogging bottoms, harem pants or jeans with a stretchy waistband.
Some nappies are of course bulkier than others. On a newborn the Bambams, Lil Joeys or folded muslins make the slimmest nappies.