Which common blades should I hold on to?

In general, you can get rid of whatever you want. However, here are the guidelines I follow for if I should release a blade:

• Do I have enough of this field skill to pass a check if they randomly come up? If so, release it. My general thought here is that if I have approximately 10 that I can muster across all of my party members, that's good enough.

• Does it only have one field skill? If so, release it. I don't like single-use blades - more field skills means more utility in merc missions.

• Is it a 4 star common? Max it, then release it (for an overdrive protocol).

I can safely say that at max merc level, I probably have a hundred blade slots free per driver.

Without repeating things off of Seiyria's excellent answer, here are two more considerations:

• High strength (30 then 35+) was the most difficult merc mission requirement for me.
• Merc level 2 is fairly easy to achieve and very early in the game. I personally never hit the cap after that, although I had an endless stockpile of common cores I never used.

From my gaming experience, The only fields skills that I frequently not have enough are elemental skills.
This is because unique Blades rarely have elemental nodes.

So I basically only keep blades with (potential) level3 elemental nodes. The only exception to this rule was if the blade have two or more other level 3 fields.

To add to the already excellent answers;

I tend to keep common blades who have the field skills that the uniques don't get; things like Production Mastery, Industry Mastery, Transport Mastery as popping a few of those on a relevant merc mission can really decrease the time needed to complete.