From a DIY, limited resources and limited manpower standpoint, a good way to get started is by acquiring basic tool donations from a couple bike shops that are supportive of your efforts, and begin by hosting pop-up bike repair clinics in parks, near metro stations, places that cyclists frequent - that way you can start to help the community and generate some donations and spread the word about your organization.
This is how we started the Valley Bikery in the San Fernando Valley (Los Angeles), with basically no seed money. We didn't require a fee to do tune-ups and repairs at our mobile stations, but we stated that we were accepting donations and working towards a brick-and-mortar location. Our most successful pop up location was in a park alongside a heavily used bike path, best timing was Sunday mornings/afternoon. We had a BBQ fundraiser, sold burgers & dogs donated by people who believed in the project, and conducted a very useful survey to gauge people's needs, volunteer interest, skill level, and location so we could start a newsletter and build a volunteer base before we had an actual space. We held regular meetings at a pizza joint and established some of the structural elements and went to work helping people in the community, training our volunteers, and figuring out where to best set up shop. We partnered with metro who donated patch kits and bike maps and gave us a night to set up at the plaza outside one of the train stations.
Our first space was in a bike shop that was huge, and essentially had more space than they needed. We gave them a percentage of our donations instead of a flat rental fee, which helped us establish a basic fund before we were making enough money to pay real rent. That location wasn't great, but it got us on our feet, and we eventually moved to an independent location in a more centralized area.
Don't think that you need to invest a ton of money to make it work. Build a core group of volunteers and get out into the community and show people what you can do. Table at community events. Collect donations at every opportunity. If there is another co op nearby, ask them to help train your volunteers, and offer to put in hours at their space in exchange. The Bikerowave on the west side of the city was extremely supportive in this way, and even gave us a cut of their income for the nights we came in to work at their shop (pre-arranged times). They also donated some overflow parts that they didn't really have room for. Our parts cache wasn't great at the beginning, but we facilitated the process by accepting donations at all hours to our homes, which we would then take to the co-op during our open hours. We went to the people who had stuff to give us, we asked for anything they might be able to offer.
Your resources are people, events, and places. Leverage them and you'll be OK.