Patio cover.

[Wash. state Desk Jet]

7. Here's some basic designs in wood

http://woodsshop.com/Plans/Patio-Cover/Patio-Cover-Plans.htm




On a 10' by 14 your cost would be reasonable. Metal roofing at lowe's ,home depot is fairly inexpensive. The stuff is for porch/patio overhangs,comes in 2 1/2 ' by 6' or 8' or 12' lengths. Colors-green/brown/black/silver/and a redish kind of a color. Also in fiber glass too. And if you wanted to close it in later on you are set up for that. Or you could throw ply or osb up there and use roll roofing which is inexpensive for a 10' by 14'
On the a screen porch/patio, some people close it in using framed in windows which will make the enclosure seem like an additional room add on to the house with the benefit of the outdoorsy
kind of effect. You would call it a screened in sun patio even if you use framed in windows with screens to do it !

Later on could mean a few years later !
Nail up a ledger as was said,2/10 or 2/12 ,put supports in front 4x's 4s ,throw a bean across and frame away.2x's 6's are better than 2x's 4's for that.2/8's 2/10's I dono on a 10 by 14. On a 20 by 30 second story,,sure 2/8's or 10s Actually code requires 2x's 6's here anyway. Treated wood is the way to go.A 4"by 6" beam should do it, on a 10 by 14. You can look up what code requires on that yourself in your locality.

Good luck with your project.