Teak is the most common wood for making care free outdoor furniture. It's normal to add a teak oil to the wood to keep it from turning gray, but a majority of people seek that gray look and therefor pass on the teak oil. Another wood that does really well outside is cedar. Cedar is going to be less expensive but you will need to use thicker pieces as it's not as strong as teak. You can get cedar pieces at Home Depot or Lowes, but I'm not sure the wood thsy sell is thick enough for what you would be building. I would seek out a local lumber yard, which in general would give you better prices than either big box store any way.

The question of it being affordable is a relative question. Teak is an expensive wood and cedar will cost you more than pine, but they will both last much longer and don't require paint. So if you look at the longevity of the wood, teak and cedar are worth the investment. You pay for what you get either way.

I made some adorondak chairs a while back and only used pine because they were my first round and the "test" chairs. I stained them and then clear coated them. I also got the wood from Home Depot. They are still holding up after 5-6 years but I have less faith in them each season and they are getting more wobbly as the weather takes hold of them. Had I known how well my design and the style was going to turn out, I would've invested in better wood. Live and learn.