Horatio: I belonged to Reserve JR and WOs/Sgts Messes back in the 1970s and 80s, and I was the PMC of the PPCLI Home Station Officers' Mess in 95-96, and I have to agree 100% with the posters like Grimaldus who are advising that what matters most in a mess are the people and their spirit. (That's why Messes got going in the first place) I have seen old, worn-at-the-edges Messes that were happy, partying places with great spirit and a healthy bar profit, and I've seen brand new spick-and-span Messes that were like funeral home waiting rooms. Paint and furniture do not make the difference: people do.
In my experience, what will be the decisive factor (like most things in the Army...) is leadership. This means that, starting with the CO and RSM, anybody in a leadership position at any rank encourages Mess membership to attend (even if its only for an hour, or for one drink), and most importantly set the example.
Caveat: I'm categorically NOT talking about pressuring people to drink alcohol: I grew up with that in Messes, but it was stupid and can lead to trouble. You also have to take a look at what type of events have been successful in the past, and try to do more of those and less of things that nobody likes. This sounds like a no-brainer, but you'd be surprised how this doesn't happen.
One thing I have seen done very successfully is for Messes to be open on unit armoury training weekends (if your unit has these): this will take some reasonable degree of control to make sure you don't mix booze and training, but it can be great. Example: Classic War Movie Night on Saturday, with a couple of kegs and some pizzas.
On the Public vs NPF work: be very careful. Talk to both your ASU/Bde NPF Administrator, and the CE Section that supports your unit. They can help you understand what can and can't be done Public vs Non-Public. Be careful about assuming that was done in one Mess can automatically be done in another. As an example, here in Kingston at the Fort Frontenac Officers' Mess, parts of the Mess are maintained and upgraded publicly, and parts must be done with NPF funds, and you have to know which room or facility in the Mess you're talking about. The situation over at the RMC Mess, or up at Vimy Mess, or up the street at the PWOR Mess, might not be exactly the same.
Finally, I'd be careful about the practices of rentals and encouraging a large Associate membership. Both will almost certainly bring you in lots more bucks (that was how we kept the Home Station Mess out of the red), but both have the potential to cause problems for the Regular members, who may find themselves having less and less control of their own Mess, but unable to risk the financial loss involved in controlling the problems. There is a fine balance, and it's not always easy to find.
Keeping Messes alive these days is difficult, in both the RegF and the Res. There is a ton of social competition out there that can make it hard for Messes to survive, but keep the people in mind first and you'll be OK. Good luck.
Cheers