The teams should prioritize based on the makeup of the roster and how many other free agents are available at their respective positions.
The fact that Trent Brown is considered by some to be the top OT free agent - and how sad the OL is overall - Onwenu should be the top priority. It would be nice to sign a FA OT and also draft an OT early, allowing the Pats to move Onwenu back to guard.
With both Henry and Gesicki about to become free agents, they need to re-sign at least one TE, preferably Henry.
WR is another position in need of upgrades. Don't make that task more difficult by letting Bourne walk. All you have to do is look and see what happened with the inability to re-sign Jakobi Myers results in a bad situation becoming worse.
Next would be Kyle Dugger. He is a good player and I certainly hope the Pats can re-sign him, but to me he is only priority #4. Uche would be #5, a lower priority.
With so many holes to fill, don't make the reclamation even more difficult than it already is. The Patriots have cap space to make some quality upgrades. If they can pull that off then thaey could avoid having to reach in the draft due to a dire need at a position.