But as a not for profit, we'd probably be eligible for Federal grants.
As someone with experience setting up charitable projects, I would make investigating this priority number 1.
I think you have to go this way round:
First, investigate possible
funding routes. Your plan is a great one, but it needs substantial investment. You might be able to get some funds from local donors, but really you're going to need a big cash injection from somewhere to get off the ground. If your lucky, there's a local millionaire's widow looking for someone to betroth her hordes to. If not, you'll have to do it the hard way. But you do need to find out whether its really feasible.
Second, you need to put a 'package' together to sell to potential donors. That means doing all the things you listed, as well as developing a realistic sustainability plan
which shows in detail how much money you will need to set the library up and for long term upkeep, and how you plan to achieve this funding. Donors will not be interested in donating to a project which they do not see as sustainable and want concrete numbers to convince them. Get help from business advisers if you're not good with numbers / presentations etc and tap your contacts at other libraries to help you work out the numbers.
You also need to focus on how it will be helpful
and prove that there is a demand / need for it. Polls, petitions, interviews, quotes from authoritative figures like mayors and school heads all really help with this. You need to prepare to really sell your plan. This is key to any proposal.
So basically, step two is to make a detailed paper plan of exactly what the library will look like, where it will be, what will be in it, who will use it, why it will benefit people, who will staff it and how it will be funded, and who will be responsible for it. If you don't know these things, potential funding groups will barely give you the light of day (I've been there, so I know).
Third, you need to take this plan to the people who you think could fund the library (e.g. federal grants agencies, lottery funds, rotary clubs etc) and use it to convince them to back you and your plan. Trust me, in the non profit sector, money is still everything. Especially these days, the charity funding sector is incredibly competitive. Presenting to funding groups or potential donors can be really intimidating. They can ask you all sorts of questions, argue about any statistics or figures you give them, ask you 'what your basis for thinking x will cost y is', asking you whether your idea is just 'something you want to do to make yourself feel good' or whether its really for the benefit of others. You have to know the answer to these things, or they smile at you sweetly and advise you to 'go and do a bit of voluntary work instead'.
Get funding in place and everything else will come up rosy, I promise!
I wish you luck with your project!
Life is infinitely stranger than anything which the mind of man could invent. We would not dare to conceive the things which are really mere commonplaces of existence. If we could fly out of that window hand in hand, hover over this great city, gently remove the roofs, and peep in at the queer things which are going on, the strange coincidences, the plannings, the cross-purposes, the wonderful chains of events, working through generations, and leading to the most outre results, it would make all fiction with its conventionalities and foreseen conclusions most stale and unprofitable.
- Sherlock Holmes, A Case of Identity