I didn't know they did an R7 360 at 4Gb, don't you mean the R7 370 4Gb?
Either way, an R7 360 2Gb DDR5 is more than enough and an R7 370 4Gb is plenty
You will struggle with the R7 240, I wouldn't recommend it unless you are really limited budget-wise (you will be disappointed, though, if you do get it).
So R7 360 2Gb DDR5 or higher, you are good to go.
Last point, if you want to compare different cards, visit this link, scroll down and use the drop-down boxes to choose your desired specs - you will clearly see the R7240 has a 3/10 score, Vs the R7 360 with a 6/10 (anything above 5/10 and you're good to go).
Play around with the different options and GPUs, find one that you feel comfortable with, but avoid the R7 240 (LinusTechTips on Youtube will also confirm this, with an episode/rant about low-end cards).