A 120 would blow through this hole very quickly, but a 10-12,000lb machine would probably be a good compromise between cost, production, and not taking up too much space on site.
I agree with Cat's assessment. A machine of that size would be a good compromise. I wouldn't worry about your trailer, just have the rental company deliver it. The delivery charge for that size machine is certainly going to be a lot less than a 120.
I used a 323 to do this job:
https://www.heavyequipmentforums.com/Forum/showpost.php?p=14082&postcount=212
The 323 was the right machine for this job due to the tight conditions I was working in. If I remember right, each area was just under 20' x 20'. Depth was about 36" in the middle and 48" for the footer trenches. Spoils were cast off behind me and then moved with a skidsteer and stockpiled. Bewteen me not being the fastest operator (I'd rather be good than fast), and the tight conditions (had to take a bunch of time when I repositioned the excavator to make sure I didn't knock down the roof), it took two 8-hour days with me doing everything (layout, grade checking, excavator, and skidsteer). I ran into shale and had to spend some time in the trench to bust it up because the machine didn't have enough power/weight to do it on it's own.
As others have already said, a 323 is going to be a little small for what you want to do. It will work, but it's going to take a while. The reach isn't going to be there if you're going 5' down. Even though the hole is going to be backfilled with gravel, you're still going to have to be close on your grade and will have to do some grading on the bottom. Whoever you're working for is going to determine the quantity of gravel they need based on the 21x21x5 dimmensions. If you end up with one end of your hole way off from the other, they're going to be putting in more gravel than they figured and you're costing them money (this is the voice of experience here...:crying).
Also remember that even though this is a "by-the-hour" job, you can't let to costs get so far out of line (due to the job taking too long) that the customer feels they are not getting a good value for their money. In my area, this job is "worth" about $1300-$1500 dollars, since lots of guys would come in and knock this out with a full-size TLB in a day. You can charge whatever price you want, but if it's significantly higher than what the market will bear, you might not get many call-backs.
Good luck, and let us know how it works out...oh yea, and take a bunch of pictures to share with the class...:thumbsup
Hey Digger, what's my cut of the consulting fees :waving ?
Joe