If you liked the tree in that location, just allow the suckers to grow. After one of them establishes itself as the strongest leader, prune all the others out and only allow the one to grow. You will grow a new tree much faster than starting out from a seed or small sapling, because that tree will have already developed an extensive root system to feed the top growth.
Of course, if you have a fundamental problem with the root system, like armillaria root rot, that won't work. You probably wouldn't be growing any suckers if the roots were at fault for the tree's failure, however.
I like to prune the extra shoots out when they get about 4 feet tall and remain less than 1 inch in diameter. Using this technique, I have new ash trees growing all over town, and I have a few redbuds that are beginning to look like fully mature trees. This works particularly well for local government facilities that I service, who have no "replanting" budget and never wanted to say goodby to the trees that were failing.
I did advise them that the borers were still going to kill off their ash trees if they didn't do some treatments in the future. Curiously, they seem to be treating the borer problem like a way to keep their trees from getting oversized. Just let 'em grow for 20 years, then cut down and start from the roots again.
