Almost any telescope is appropriate for M13—it is bright enough high focal-ratio SCTs and it is large enough for small refractors.
A small refractor will show a brilliant globe floating in the blackness of space. With sufficient exposure time, you might be able to capture the galaxy NGC 6207 in the same field.
A long-focal-length SCT will resolve hundreds of stars in M13's core. The cluster will look like a teaming metropolis of stars.
As always, a rich-field Newtonian is a good compromise.