An excavator or a small backhoe. I sell Home Depot the Kubota BX TLB . It is small and compact and easy to use. The problem with a trencher is it is hard to handle, gets muddy quick and doesn't have the ability to do your backfilling and final grade. A small backhoe can accomplish all of these things. The size of your project should be a couple days. Hard to do that in 1 day as a new operator.

 

Why does the trench need to be 8"? That seems excessive. Anytime I do trenching, I rent a trencher (we own a backhoe). Trenchers are a workout (unless you get the ride-on kind), no doubt, but it digs the trench in the most effective way - you get a 3" trench for 2" pipe, not a 12" trench for 2" pipe. I've done both irrigation installs and drainage installs, and I always use a trencher. Additionally, I would also say that, even with a smaller hoe, you're going to take some time getting the controls down, whereas the trencher is straight forward - a trenching shovel will help with the fallback.

 

Why does the trench need to be 8"? That seems excessive.

I'm just following how NDS says you should construct a french drain

 

The ******* in me would be tempted to hire a few high school kids and have them dig it with shovels.
Tear up your yard less too.

 

I would go with the mini-excavator or a mini-TLB over the trencher. The mini-excavator will dig circles around the TLB and I find the controls to be smoother on the excavator. The advantage to the mini-TLB is the loader to move the spoils and then bring in stone.

I think the perfect pairing would be a mini-excavator along with a tracked mini-skid steer, but not sure you want to pay the rental on two machines.