Typical rocket have two stages, and you are correct that pretty much all the first stages take off vertically.
It *is* possible to build a rocket-propelled plane as the first stage of a two stage rocket – there’s a company named Dawn Aerospace in New Zealand trying to do exactly that.
Wings help a little because you gain a little from their lift right when you take off and you can glide down and land easily when you return to the earth. On the other hand, wings and landing gear are heavy.
So it’s not clear which is better.
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