I definitely understand the library situation; one solution might be to allow [3-year-old daughter] to pick one book herself, and you could come prepared with a set list of additional books you want to get (some libraries even let you put them on hold online to pickup when you get there). I've compiled a list of book lists and book blogs that I've found to be reliable guides here: http://listography.com/Our friend asked about the Five-In-A-Row method, so I responded to that question and also shared some further thoughts on curriculum and unschool for preschoolers:
FannyHarville/blogs/kids__ book_blogs_and_reading_lists . I like to browse them and write down titles. Jim Trelease's Read-Aloud Handbook is a good resource. The Charlotte Mason perspective is that less is more and there's nothing wrong with rereading the favorite books over and over rather than looking for new picture books.
I was especially impressed with our friend's awareness of how her own personality and training inform her thoughts about homeschool. As an engineer, she's a problem-solver. How will that help or hinder her as a homeschooling parent? In developing the approach we take (which is of course ever evolving), we don't only consider what works for N. (although that is a crucial priority), but also what works for Tim (and to a lesser extent, for me). For example, I like the idea of the "project-based" approach but it's not Tim's style. And I've written before about the failure of my attempt to impose a structured form of record-keeping; we had to adopt something more organic to Tim and N.'s days. Learning at home is a collaborative process that requires awareness of both parent and child's temperaments and learning styles. Furthermore our approach to learning at home is always subject to modification and adaptation as we get inspired by a method or material, as life conditions change, as we build on what works and jettison what doesn't. I call this blog "Unschool Academy" to capture this sense of hybridity, that we are inspired by unschool principles but that our days are often more structured than perhaps those of others who identify as unschoolers. And I always point to Melissa Wiley's "tidal homeschooling" concept which so aptly captures the true ebb and flow of homeschool that many curricula and methods can't accommodate. You can pick a method, but in real life it seems that many people make use of bits of many different approaches.
As for Five-In-A-Row, I would definitely print out the book lists and use them; they are good, quality books! I personally wouldn't want to follow the curriculum because I don't think you need a curriculum for pre-school, but I can totally understand wanting to feel like you are "doing something" and I could see FIAR meeting this need effectively and simply. In other words, if you have to use a curriculum, that seems like a reasonable one to use, and not too time consuming or too academic. A blog that has a lot of pre-school-age easy home activities that build numeracy and letter familiarity is "What Do We Do All Day." I notice she just put up a good post about how to find good children's books too!
I do feel strongly, however, that pre-school kids need most of all lots of unstructured play time. I think the best investments are not in curriculum but in open-ended play toys: dress-up clothes (from thrift stores rather than pre-fab costumes), blocks, dolls, etc. Lots of outside time. The hardest thing I thought about being an adult in a small child's world is that we want to accomplish tangible things with our days, but kids accomplish what they need developmentally through what sometimes looks like doing nothing at all. Big blocks of unstructured time can be hard for the parent but I think they are really good for kids, developing their long attention spans even more and helping them learn how to draw on their own resources and interests.
A neat approach that is related to this idea is "project-based" or Reggio Emilia schooling, in which your kids pick a topic they want to explore and every day spend a little bit of time on it. Say, butterflies. You'd pick books together from the library about butterflies and read them. You'd ask your daughter for her ideas for butterfly related projects: a dance, drawings, making up a story, etc. In some ways we do this (though not explicitly) in the sense that we are always looking for ways to build on N.'s love of trains and buildings.
More important than choosing a method or curriculum, then, is to identify the temperamental requirements of both you and your child(ren), to identify the principles that have led you to homeschool, to identify a few broad goals (for example, for us for a preschool-aged child, these would include daily reading aloud, daily unstructured play), and to practice regular reflection and analysis to determine if your homeschool days are fulfilling all of the above. One of the things I love about homeschooling is this process, this continual engagement in thinking about the why and how of learning.