Wonderful looking tree. Definitely has potential. Dave has given you great advice. He grows in Minnesota, a cold climate like mine. Poink is in Texas, where summer heat is a much bigger problem than winter cold. You are in New Jersey, warmer than Minnesota, cooler than Texas. Barberry should do really well for you. It should be fully winter hardy, if it doesn't dry out you should not loose branches over the winter.
On freshly collected deciduous material, my preference is to first do root work and not worry much about the 'above ground' stuff. Generally I believe near to bare rooting collected deciduous material is the way to go. No point bringing along quantities of 'bad soil' to be a problem to be corrected later. Growing anything in a pot is an artificial system, we need to make sure there is air and water to the roots, the fine clay based nature of most 'natural' soils just does not work well in a pot, so don't bring that problem along by leaving a lot of old clay based 'dirt' on a freshly collected tree. Hose the native soil off, gently, without breaking off fine roots. If it looks like taking soil off is breaking fine roots, stop. Either switch methods of soil removal (go to using water instead of hands) or just leave the clods of collected soil.
Modest amount of native soil that is 'stuck' to the freshly collected deciduous tree, if the remaining amount is somewhere around 1/10th or so, of the total soil content of the pot, the collected soil should not be a problem. You don't have to scrub the roots clean.
Prepare the pot with sreens over drainage holes and put in place wires to tie the tree firmly into the pot.
Trim the roots back some, get rid of long roots that would have to be wound around and around in order to fit into the pot. Barberry do root from cuttings well, old wood can put out new roots, you can remove a major portion of the root system and it will grow a new one, no problem.
Put down the first layer of bonsai potting mix, place the tree, back fill to about 3/4 depth, work mix into air pockets. Fill in the voids. Then tie the tree in with the wires. Crank it down tight so it won't wobble even in a stiff breeze. Then finish filling in the potting mix.
You should not get movement when you gently try to wiggle the trunk. This is important, because movement caused by wind or squirrels or the neighbor's cat brushing against branches may cause a tree that is not tied tight to wobble in the pot, breaking all the newly forming roots, setting the tree back further and perhaps causing death of the tree. If tied in tight, by the end of the first summer you should have a nice good set of roots to carry the tree through to next Spring.
After care is important. After collecting, keep the tree in bright shade for the entire spring and into the summer. Only after you see lots of new growth would you move it into the sun. If it seems to not be doing much except making a few leaves, keep it shaded. It is growing roots. The new buds and branches won't extend much until it has enough roots to feed them. But you leave a lot of branches becuase they feed the roots. So even though you may have radically chopped the root system, I would only do a modest prune back of the branches right after collecting. Balance branches to roots some, but leave quite a bit more branches than you think the roots could support, you want there to be enough branches to send the hormonal signal to 'make roots now!' The branches will send sugars and nutrients down to the roots, so if you want a healthy root system keep a large number of branches.
Let the tree grow for a year. If you have a good bonsai potting mix you won't need to repot next spring. You have a nice mature trunk, repotting most likely won't be needed more than once every 2 or 3 years. The second year is when you can start going to town with working the branches and the rest of the tree.
Those are my thoughts. Look at the tree actually in front of you. If my advise makes sense, follow it. If you have reason to think otherwise, remember, I don't see the tree you actually have in front of you. My advice might not be on track.
About the size, 30 inches is a nice size for bonsai. Trees this big get a lot of attention at shows and exhibits. You have marvelous bark on this tree. It has presence, don't worry about it being too big. Besides, next year when you start working on refining this tree, the size will come down significantly. Don't worry about size, you have a great trunk, that's the important part.
About suckers. You have a great old trunk. Suckers compete with the trunk for water from the roots. Remove new suckers right away to keep the main trunk healthy. You might keep ones you feel are positioned right to make secondary trunks, but your main trunk is fantastic, don't need anything to distract from seeing the main trunk.
