I am part of a building planning team at church. We are adding a new building that will have heat/AC and a kitchen. The existing buildings are all single phase. A member, who is an electrician, is urging us to convert to three phase. However, I do not see the need. The three phase is available, but I just can't justify doing this for the new building. Is it worth it to go three phase? What are the benefits? What about all of the existing single phase equipment/lighting?

I would stay with Single Phase.

Honestly, before just assuming single phase is best, really need to know the size of the building, amount of lighting, type of lighting, exterior and parking lot lighting, size of AC and any electric heat, will an elevator be needed, cooking equipment, any possible future addition, any other items of large loads iI did not mention.

Agreed, I was Assuming a Small church. Not enough info.
Also, what size panel(s) do you have now?

Three phase generally is used when the power supplied by the utility justifies it and there are motor loads over 5 HP. The single phase stuff will likely still work, but the new single phase voltage may be 208 vs 240.

Wiring can be cheaper for 3 phase when large loads are involved.

The utility can force you to upgrade.

The building will be two story with an elevator. Total of 20,000 sf, 16 separate classrooms upstairs, kitchen and fellowship area/seating for 340downstairs. The existing facility is gas heat. Long term plans would include a new sanctuary (don't know how big, probably seating for 700).

I know there a lot of unknowns. I suppose we could have a 3-phase elevator and AC, and run everything else single phase? Would that make sense?

Go with 3 phase, assuming 120/208 volt system, certainly due to the elevator, and use it for anything possible, HVAC, etc. Some kitchen equipment may be large enough to take advantage of the 3 phase.

Interior lighting can be 120 volt, and exterior lighting can be 208.

You may even consdier using 277/480 volt. All 3 phase equipment can be 480 volt, and al llighting can be 277 volt. Transfomers will be need for 120/208 volt distribution for all 120 volt loads, such as receptacles and misc.

Judging by the square foot, and possible future, I would be leaning towards the 277/480 volt 3 phase system.

For critical or expensive 3 phase motors be sure to have undervoltage and loss of phase protection. I've been very happy with the "Motor Saver" line of products: SymCom

I also like squared's combo overload relay, fuse and disconnect switches.