I am having issues with lag due to quarries from some of the players on my server. What is the best method (or mod) to use for a quarry with the least amount of issues?
When you say lag, what in particular do you mean? I am guessing that your issue is probably due to someone miss-guided flooded the quarry or the quarry unearthed some kind of fluid. All the liquid updates is really bad for the server and clients in range. You really should force people to use either the Ender-Quarry or QuarryPlus+PumpPlus instead to deal with fluids.
The MFR laser drill(combined with a cobblegen) could of course completely eliminate the need to quarry as such, but I am not sure that the infrastructure needed to run enough of them to compare to a quarry is a worthwhile tradeoff.
The Ender Quarry from extra utilities was designed for optimal server performance. It only loads the chunk it's working on. So a well-build quarry will only have like two or three chunks loaded at a time.
Chunkloading the 17 chunks a normal BC quarry loads in which nothing except quarrying takes place should not be causing any serious problems. Definitely not any lag issues. It is true that enough quarries will count up the total amount of RAM needed on the server, and in that respect is is a good idea to use either Enderquarry or QuarryPlus that only loads a few chunks instead of them all.