You should decide how high of quality you want you tournament to be. As others have said, for affordable non-USTA tournaments make the event nice and laid back and have people bring their own can of balls. You don't really have to worry about singles sticks either.
For USTA tournaments, if you are charging enough then you should be providing most everything. High quality balls (championship quality, good endurance), water, singles sticks if you can, other nice things like Gatorade, fruit, etc. Basically, the more you charge the more you should be providing so people want to do it again next year.
Either way, you should definitely use TDM
to help with your scheduling. You can input all the players manually and have it create draws and schedule automatically for you. If your event is on TennisLink it will download all the players for you (except for those who register by mail). Although to do that you have to get "Tournament Director" status from your section.
TDM has an option for scheduling called the Garman system which helps avoid having as many open courts (but leads to a little more waiting sometimes), it also allows you to choose what you think the average match time for each event will be. Since I usually have open courts when I run my events I just let the average be 2 hours and go with block scheduling and people like it because they never have to wait for a court to open. But if you have big draws and not many courts you will need to squeeze them in as best you can.
Back to the insurance, that's great the facility isn't requiring that from you. Oftentimes the facility will hold you liable for some certain amount for damage to the property even though they don't require proof of insurance, so you should check that out. I would suggest you at least look into a few insurance quotes even if you decide not to get any. While the facility may not hold you responsible for damages, a player who gets hurt during the tournament could try to get some money from you. It's very rare, but still...you can always limit your risk by making a waiver and having all the players sign it before their first match.
Once you get past all the headaches of organization I'd be happy to help you work out the scheduling.