If you want to save the seeds from your squash, but are concerned about cross pollination and growing some freakish veggie the following year, the answer is simple:
Squash only cross with others in the same species; so if you choose only one from each species, you can rest assured.
Unless your neighbor is growing squash, then I can't help you.
Simply choose one from each group:
Curcubita pepo (the most popular)
Most Pumpkins, all summer squash inc. yellow squash and zucchini, many winter squashes including Acorn, Delicata, Tuffy, Sweet Dumpling, Honeybear, Spaghetti Squash
Most of the Kabochas and Hubbards, Buttercups, Australian Butter, Big Max Pumpkin, Pink Banana
Butternut varieties, Black Futsu, most of the Crooknecks, Kikuz
Cushaw varieties, Hindu White Crookneck Pumpkin, Japanese Pie, Tenessee Sweet Potato
The list goes on, really there are so many types of squash that it would be fun to add a new type from one group each year. This would also insure that you maintain a good supply of seeds.
Remember also to choose a variety that is either an heirloom or open pollinated, not a hybrid, for saving seeds. Also, beware of volunteer squash coming from the compost.
Some seed companies that give you the plants' botanical names include Seed Savers Exchange, Johnny's Select Seeds, Baker Creek, and Territorial Seed Company. You'll notice that in many cases the first part of the name is abbreviated, such as C. pepo and C. mixta. Having this information at hand makes planning much easier.
Here's how to grow a variety of squash vertically.