This is how I can see the inclusion of Rick Jones working well in this movie with elements of the TV Show and comic.
Rick Jones is an arrogant, bad boy like student at an university. He has a class to attend where he is going to be shown a Gamma Transponder made by a Doctor Bruce Banner. He thinks this is going to be boring by just hearing about it.
He is in the class along with some other students who are really excited. Banner demonstrates the Gamma Transponder to the students by sitting in it and turning it on but doesn't fire the gamma radiation through himself. He tells the class why he made the machine and what the effects of Gamma Radiation are to a human, death.
The lecture ends and the students leave all real excited and happy. Rick however found the whole thing a waste of time but stays behind to mess about. Banner is in the lab but to one side doing some other lab work unaware that Rick is still in the lab. Rick goes over to the Gamma Transponder, plays around with it and causes it to malfunction. An alarm goes off alerting Banner and everyone else in the university like Betty and General Ross.
Banner see's what Rick has done and tries to fix what Rick did but it isn't working. The machine starts to get loud and smoke is coming from it. And a Gamma Radiation firing in 10 seconds countdown starts. Banner rushes over to Rick. Grabs him, makes him wear some lead lined clothing to stop the Gamma Radiation harming him but before Banner can get his on the machine fires the Gamma Radiation and explodes. As it exploded, Ross and Betty just entered the lab. Betty is hurt by the fire and explosion, Rick is knocked out but not harmed by the Gamma Radiation and Ross is clutching his arm and looking at Banner's motionless body and then looking back at Betty who is hurt. This makes Ross angry and gives him even more reason why Banner shouldn't be with Betty as he blames Banner for what has happened to Betty.
Then later on, Banner is ok and not dead as he should be after taking a leathel dose of Gamma Radiation but is safe as he tested a very small amount Super Soldier Serum on himself a couple of days earlier.
Then with Ross after Banner and because of what Banner has become, Rick feels guilty and owes Banner big time for saving his life.
There, finished. A pretty good origin and inclusion of Rick Jones by me!