I do 20 gallon all grain at our northern home and 5 gallon extract at our winter condo retreat. It is nice to do a full volume boil but due to space restrictions at the condo, I do about 3 gallons and top it up. Got to go with what ya got sometimes. It keeps me in homebrew that is good. Maybe not as much control as with AG but still made it myself.
As to boiling it outside. I have been doing that for over 20 years with no problems. With a little common sense precaution you will have no contamination problems. In the event of a boil over a garden hose solves the clean up mess problem. Even at our condo I use an electric hot plate sometimes outdoors. It's painfully slow but gets the job done and no fear of wort running down the side of the electric range. Keeps the wife happy and you know the old saying about happy wife.
To cool the wort I still use the ice bath method for extract. There are coin operated ice machines down here that dispense 20lb bags of ice for a good price. That about fills a large sink with the kettle in it.
Consider how far you will go brewing. most of us started small and bout equipment for the next step then did it again. I went from a Mr Beer to 5 gallon extract to 5 gallon AG to 10 gallon AG to 20 gallon AG with a seasonal side of 5 gallon extract. There was a lot of equipment change from the beginning to now. Could have saved a lot if I started with the big stuff.
You will enjoy going larger. More beer in about the same amount of time. Good luck.