Go into a recently finished lower level/ basement and look up.  Will you see painted drywall or ceiling tiles on a grid, known as a drop or suspended ceiling?  Chances are good it will be drywall.  How about one from 20 years ago?  Chances are it is a drop.  That's the direction ceilings are moving.  We bought our house 20 years ago with a drop ceiling in the finished part  of the basement.  When we renovated it this year, the decision was easy to have drywall installed.  It becomes rather obvious after walking thru hundreds of homes, so you can take my word for it - this is what buyers will want in the foreseeable future, a basement that does not look like a basement. 

Reasons given for staying with drop include easy access to pipes and wiring, by far number one.  Followed by easier to install for DIYers; lower cost (?); and more design choices.  Reasons for drywall include much better appearance, by far number one.  Followed by higher ceiling height; matches rest of home style; and better resale value.  You will need to decide which is better for you, but I implore you to go with drywall, as my guess is 75% (and climbing) of owners are going this way.  Yours will stand out that much more in the future if it is drop style.  If you need help deciding, get 2 or 3 bids and ask the contractor for pros and cons.  When I considered how often I had to access underneath the main floor joists over the last 20 years that was not in the unfinished area or would not have an access panel for a shut off, it was very infrequent.  The cost of installing it was not all that much, I am estimating it cost $1600 for 750 sq ft of ceiling for materials and labor, as it was lumped in with the other drywall areas.  How much would that area cost for a drop?  I am getting online estimates starting at $1000 for materials and labor and going up sharply.  It may even cost you more to pay for a drop ceiling to be installed, although if you can do a professionally looking job yourself, you should be able to keep it under.  But for the amount of $500-750 of savings, is it worth it?  I estimate a gain of $2000 in an average price home by having the ceiling drywall vs drop upon selling the house, and $5000-7000 on a large home.  More if your ceiling tiles are over 20 years old.  Even with paying a contractor to break into your new ceiling to fix a leak or run wiring, and someone to repair it, I believe you are still coming out ahead in the end, plus the enjoyment factor in the meantime.  You can compromise by drywalling the main part and do the drop in one room where you need more access to things. 

The lighting may cost you as much as the ceiling finish.  Can lighting is used almost exclusively now in lower levels, whether drywall or drop.  This is a nice improvement from the 4 foot fluorescent fixtures from years past, so at least install cans as part of your lower level renovation project.  You may be able to save some money buying and installing the fixtures yourself, and have the electrician run the wiring.  But if something goes wrong after the drywall is installed, oh boy.  I just paid the electrician to do all of it for proper spacing and to head off future problems. 

Happy drywalling!