Don't try to go too big, too soon. I advise you to not build a greenhouse until you have a better idea of how much you like it.
Start small. Get some lilies from a garden center or catalog; a pack of 5 or 6 is good to start with (preferably not in bloom!). With vegetables, I would wait until late April to mid May and go to a Lowes or Home Depot and get some of their veggie plants that are ready to go into the ground. Tomatoes are easy, but cucumbers and squash are climbers, so if you don't have a trellis ready for them, you will need a lot of ground space.
Get, and keep, the areas you want your plants in weed-free. Depending on how well you do, you may have to hand-pick weeds daily, or at least twice a week in the summer. I don't know what kind of soil is in your area, but you may have to supplement yours with bagged soil from a garden center. You could also start 'collecting' organic matter (old salad, potato and banana peels, apple cores, etc) from your kitchen in a plastic, lidded container and take these things out to your plants' soon-to-be homes, dig the holes and cover it up with dirt and add a layer of leaves or even old newspaper. Earthworms will be attracted to the cool, moist food source and will come to eat and leave castings, aka black gold for plants.
As far as the dogs go, if you want this to be fun and rewarding, you're going to have to get them under control in your yard. You could put up a small fence around your gardening area. I don't know how well-behaved thay are; only you know what you will have to do to keep them from destroying the garden.
Gardening is very addictive. I know I don't need any more plants, and I really don't have the space prepared (yet), but whenever spring comes and the garden centers come to life again, I can't help myself. I have to at least browse. Take little steps, don't beat yourself up for making mistakes and see how resilient plants are.
The knowledge/experience you gain from this growing season will make next year even more fun and exciting. If you ever have any questions, feel free to contact me. Good luck!
