Since it will be on its own roots, it will take a very long time before it begins producing fruit, and most likely the fruit won't be that good and the texture will be a little mealy. I'm not an expert on apple rootstock but it might be more closely related to crabapple than the type of apple you are familiar with.

I encourage people to plant own-root fruit trees, if they have the room (and patience), but growing a rootstock variety is a waste.

It's generally recommended to remove all suckers below the graft point as it's the root stock attempting to push growth. Like Parker mentioned, the resulting fruit is usually of sub-par quality. The root stock was bred for hardiness, disease resistance, etc and not necessarily for the quality of the fruit.

Root stock doesn't necessarily produce desirable fruits. Do you really want to wait years to learn that you have a dud?

You didn't say how long it's been int he ground. But my guess is that it hasn't been very long. Why not take the leap and get a fresh start with a new tree?

Just one point "I'm assuming they're from the rootstock and won't be a dwarf or semidwarf, " It is the rootstock which makes the tree dwarf or semi-dwarf so those suckers will exhibit the same characteristics but the fruit will be an unknown quantity. The palatable scion apple is lost.

Thanks for the responses. Will elilminate it. One less tree to mow around, anyway.....:-)

Yes, apples are one of the easier trees to graft if you have never done it before.

I agree, the rootstock is the part that makes the tree dwarf so any apple you graft on this will also become dwarf. I would graft it over or get someone to do it as the roots are already established, unless you don't want an apple tree at all.

It will depend on what zone you are in if you can grow an apple on it's own roots, I surely can't unless it is a crab apple.

Seems like you have a vigorous rootstock that likes your soil, if it's pushing up shoots after a trauma like being ripped out of the ground. A good option that Konrad suggests is to let one of the shoots get to about thumb-width, then graft a desirable variety onto it (unless, as ubro suggests, you don't want an apple tree at all). I had a similar situation with a pakistan mulberry this year, long story short I have a single mystery-root-stock shoot that I'm letting grow (trimming all other shoots off) so that I can graft a new pakistan mulberry onto it next spring. The roots will at that point be well established and it will do much better than a brand-new pre-grafted pakistan mulberry.