I have been building and fabricating for nearly 40 years now,
and I jsut finished a backhoe of my own design, I first bought 2 or 3, sets of plans and down loaded a few free plans as well, and down loaded pictures from eBay and many many pictures off the net, to study designs and ideas, and also started to collect parts manuals and part books,
also down load or get brochures from many manufactures, usually the pictures are nearly a set of plans, Grid them and then enlarge them,
How To Enlarge a Drawing Using a Grid | eHow.com
Drawing Using a Grid
if you copy an existing design you will benefit your self, by letting some one else do much of the design work,
much of the cylinder size, needs to be balanced with the strength of the materials one uses, and design, if one uses short strokes one will need larger cylinders and if one uses long stroke cylinders they can be smaller as you will have more travel and be using more leverage, and the hydraulic pressures one uses.
so to answer your question is not some thing one can do with a lot more information, and know the design and what your wanting to have for power, and abilities,
your dealing with a "large" backhoe for a home built unit with those dimensions,
but one could built it with 2,1/2" cylinders and one could built it with 5" cylinders, and both will dig, and depending on the materials one uses, you may jsut bend it in to scrap iron or it may be under powered, some will depend on the strokes you chose as well. and the leverage one designers into the machine,
again being 15, the back hoe project I jsut finished would have overwhelmed me at that age, and I do feel I have above average mechanical ability, and was a fair welder that that age.
first one needs to consider the cost, and it my be that your independent wealthy, but I used 95% scrap iron out of some old machinery to built my machine, so the steel was not much of an issue, but the hydraulics cost me close to $2000 before I was done, cylinders, valves, fittings, tubing, hoses, etc,
my recommendation is to get a set of plans if your serious, and follow them or enlarge them a few percent to get the unit your desiring,
(personally I think that may be a real challenge for you and my guess of your skills),
if your really intent on it, search EBay or wrecking or scraping yards, or other, and buy a junker and rebuilt it, new bushings and or cut our and have new bushing made and weld them in, and rebuilt the hydraulics, it will be probly be cheaper than buying steel.
IF your intent on doing this, study a multitude of designs, get basic books on basic hydraulics and principles,
and get a friend that is a good fabricator and buddy up with them so they can mentor you, and listen to there guidance, learn and learn and learn some more, study and study, you will be benefited if you have access to a machine shop as well, a minimum of a large drill press capable of drilling up to 2,1/2" holes, a set of large reamers, for reaming and aligning of the pivot points, and reaming out bushing stock, and other.
If you do one from scratch you will encounter many many obstacles in the construction of
see here is a 'lighter duty hoe" the reach is close to what your wanting to build,
Truckhoe&Towable Truckhoe - Versatile Backhoe Alternative
it is using 25 gallon a min, hydraulics
a heavy duty unit would take much more,
an unless you have a fairly hefty skid steer loader that is a lot of back hoe, and you would probly need stabilizers as well, to use it efficiency,
mine is smaller than what your design parameters are as you stated them, (not a micro) but I have it mounted on a 8000 pound 100 hp tractor, and if you do not put the stabilizers now it will shake the tractor all over, (it has a sub frame),
attached is a picture of the unit I jsut finished,