The important thing with the D3xxx & D5xxx cameras is making sure that the lens has an in-built focus motor, as your camera body doesn't have this.
For Nikkor lenses, these are AF-S
Sigma these are HSM
and Tamron uses USD
Make sure the lens has the USD designation, or you will only be able to focus manually.
The Tamron abbrviations can be found here:-
Tamron Technology Section, Tamron USA, Inc.
It looks like Tamron have both USD and non-USD versions, so take care.