PCB Size and Placement Issue
The first thing would be to add up all of the areas (or group them in altium) and see what area they take up, your board needs to be bigger than this area. 

You also need to account for via's and traces, I'd add 20% to 40% of the component area but this is what I do, and is design dependent. Remember that the time it takes you to route is also a cost, and on low quantity boards it might not save you any money to make the board smaller.

The last thing would be to remember that if you want a silkscreen with printed reference designators, this will take some additional room (although not much because you can print this over traces.)