resistance and uncharted do follow on so yes you would be better starting at the beggining of the series.
you do not need to play bfbc2 before bf3 as you will learn as you go in bf3.
its up to you which game to play bf3 or mw3, i have bf3 and will be getting mw3. bf3 is a better game and requires more skill to get good results. mw3 will be the same as mw2, good game but anyone can play it and get kills also cod is getting a bit boring now , same thing every year. but the spec ops in mw3 is good if you have a friend to play it with. they both also have good single player stories, modern warfare however is a continuing story so you would probably have to play modern warfare 1 and mw2 to pick up the story.
you should also give assasins creed a go. first one is a bit repetative, but the rest of the series is quite simply brilliant always gets 90%+ in reviews.
oh and if you play online you may sometimes do this
hope this helps!!