I like to combine the DI (if it has one) and a mic. I have had good luck with an AT 4040 on a mando. If it's a good instrument (loud and well played, too), you should have a lot of options. The worst is if they move around a lot (and the DI can be a lifesaver in this department.)

SD mics are nice, as well. I've used the SP C4's a few times as well, with pretty good results.

Hi, Bob:
I have to deal with mandolins in a very similar manner as you are. I do live CC on Friday nights at a very large facility (2500+), and on Sundays at a much smaller facility on a 'mobile basis' as their permanent site is under construction. Plus, I have recorded many bluegrass groups over the years.
Personally, I like SDCs. At the 'big gig', I have the use of Shure SM81s for acoustic instruments, and that works well on the custom-made 'F'-type mandolin played there. Our board is a Midas Heritage 3000, so the onboard pre is fine for the detail and definition required.
On the mobile gig, I use one of my NT5s on an ancient no-name 'A'-style
(teardrop, but with 'F' holes) mando that the music director (a former luthier) did a great job setting up. That goes into an A&H GL2400, which is OK. If I want better detail for recording that, I have a Grace 101 ready.
I have also had good results with a fairly obscure mic, the E-V RE-200. This is a front-address mid-sized capsule (about the size of a nickel) 'real'
(i.e., externally-polarized element) condenser that they still list on their website. I bought a couple about 5 years ago from a church that was upgrading to DPA mics (!). The larger capsule is great on "oval-hole" mandolins and mandolinos, with their added bass. You can sometimes find e-bay deals on these (I paid $200/pair!).
Finally, the A-T 4041 is good on anything you'd use an SM81 on. Check out the post by Tom Bethel, "Mics and Stuff" in Buy&Sell. He listed some gear for sale, including (3) AT4041 at around $169 apiece. This was in the last week or so, and he had the e-bay address on it. PM him, see what he's got left. Tell him I sent you....I want another one myself!
And you're right about what a mandolin can add to the fray. Sweet music!

Used the NT5 in church today, and it went very well. Experimented with the sound from the f-hole vs. something closer to the strings. I liked the woodier sound by the f hold, but I let him experiment. I was playing keys and didn't really notice what he settled on. But he sounded good in the mix. Thanks for the help.

The NT-5 is a very under-rated mic, IMHO. I bought mine to replace a pair of AKG C452EBs that were stolen many years ago. Very close sound. And then they come out with the NT-55 !!!! Now I have to figure out how to score a pair of THOSE!!!!