How many playthroughs do I need to buy everything?

You may be able to get everything on the second play through. The reason for this is you should be able to buy everything from the stores in game with the 800k. The weapon upgrades, you could probably level them up some also, mainly stick with the main ones you use until you have spare cash for team mates weapons. On your second playthrough each time you pick up a weapon it will gain 3 levels automatically.

Example is the Saber assault rifle, you dont get that until the 3rd to last mission in cerberus HQ, so on your second play through you can only max it out at 7, as soon as you pick it up a second time it will automatically got to 10. For some of the weapons that you find earlier in the game, they can go from 5 to 8, so you only have to pay for 9 and 10. I do not remember the cost of upgrading the weapons from 8 to 10, I want to say 150k to go from 9 to 10.