Paul's right. Your option of taking someone on or setting up with a friend won't solve those late payers, they're two separate issues.
If you want to set up with a friend then you need to either look at simply working side by side, where you invoice them for work you do for their clients and they invoice you for work they do for your clients. This is how David and I did it until we went Ltd together. Or you could go into partnership, LLP or Limited, but if you're only just starting with this friend then I wouldn't recommend doing too much / setting too much up together until you know it'll work.
Taking someone on means registering as an employer for PAYE with HMRC at least (not sure if you need to register elsewhere? I left that to our accountant!). You'd then need to deal with wages, deducting tax, statutory sick pay, holiday pay etc. If the person can ensure they've got other streams of income too (which I would assume if you're looking at them only being part time for you) then I would just get them to invoice you as a freelancer/contractor rather than you paying them as a staff member, but ensure they do have other areas of income, else you can still get hit as an employer (loophole that was closed up a number of years ago I believe).
In regards to clients paying late, is this for the final part of the work you've done for them, eg. are you taking a deposit, a payment part way through (depending on the size of the project). Do you have it written into your ts and cs that if final payment isn't received then the work comes offline until it's paid for? Or is this just for ongoing maintenance type work?
If you're doing ongoing work and constantly having to chase specific clients for payment, then get them to pay an estimated figure up front. If it's for major work, remove the work whilst it's unpaid for. They've not paid for it, why should they have it? You give them an appropriate amount of time to pay and if it's not paid by the due date give them a final warning before removing the work.
Another method is to offer an incentive, a bit like utility companies do. eg. pay this bill within a week and get 5% off your next bill, or if you give them discounts on their hourly rate or hosting, just say if they don't pay on time then the discount will be revoked.
It's harsh and that's why I leave it to David to deal with as I'm a wuss
