There are a lot of things to consider. 1st, I would wait until it is dry whether you hire or do it yourself. 2nd, if you do it yourself, get a tractor w/ backhoe or a backhoe. I think you will need both the loader and the backhoe to do the job right. But, it is difficult to say without seeing your land. The backhoe will give you a nice cut edge on the ditch and depending upon elevation, this could work very nicely. If the land will flow naturally toward the ditch, this should work becasue the the water will flow down to it, collect and drain. A swale could also work, but again depends upon your land, elevation, and room. It will be larger and can help the contour if you don't have a natural flow.
3rd, I suggest having a laser transit to check elevations unless your elevation is obvious. It is easy to get too deep and have a low place that will hold water. A cheap regular transit will work if you have two people. 2-300 bucks for a selfleveling one person transit.
I added a ditch along my drive similar to what you are talking about. On the driveway side after digging, I went in with the loader and cut and back drag the side next to the road in places to make sure the water drained away from the road. Again, your land may have large rocks that with a loader may be difficult to get out, and if so, gets your work out of contour, then you have to re-work it. A backhoe will make that part much eaiser.
Box blade can also be made to work. There are other posts with pics of people using box blade to dig swale along road. The potential problem with that is you generally have to get the tractor in the swale and it takes some time to get the nack of adjusting the box blade at the right angle and depth.
4th, and probably most important is the value of your time. I don't know what you do, but if you crunch the numbers, it might be cheaper and better to simply hire it out. However, if time is not an issue, and you just want to do it, then get a backhoe.
One more thought is a skid steer. Never done it myself, but have seen it done. Turns on a dime, gets in tight places, works fast. But will end up with more of a swale than a ditch.
Good luck.