Qualifying someone as an employee vs a contractor

My wife and I have a very small catering company. We have recently gotten all of the business licenses and tax identification and things set up that we need. We have no full time employees, but we have a few people that we hire on an event by event basis and pay hourly. I do not think they qualify as contractors, but they are also not really full employees, but I suppose we could treat them as such.

As much as I would like to pay them cash under the table, I feel like we should be filing forms and doing withholdings and whatnot. I just am not sure which forms to fill out. Do I need a full W4 and I9 and everything for everyone that works for us for a weekend? I can't find any reliable resources online, and I have no idea who to go to for a consult.

I've looked at things like ADP's service and that feels like overkill, but we also don't want to get into trouble with the IRS or anything like that by not doing things properly. How do I hire and pay these kind of employees?

You should definitely take your payroll responsibilities seriously. If you don't you run the risk of having an employee file for unemployment and then the state might conclude that they could get a lot of money from you just by spending a little time on an audit.
If you want to spend some time studying you can probably handle your responsibilities with an Excel spreadsheet. Or you could go to Costco or use Quickbooks. Payroll is not complicated but it does have several parts. I do payroll for about 250 employees twice a month. The trick is to spend enough time on setup that the process is easy, reconcileable and failsafe.

I HIGHLY recommend you try Intuit Online Payroll. My firm provides back office services including payroll for numerous startup clients and this one is by far the best and easiest we've found.

Similar to ADP, look at SmallBizPayroll.com, a division of Paychex. I'm not affiliated with them at all other than being a happy customer.