Well, I'd say neither monitor nor GPU, save up for a more modern platform first.
That said - a monitor upgrade in terms of size (not concerned about the refresh or response time) might be worthwhile just because a bigger monitor would be more comfortable to view for extended periods. I've recently upgraded my monitor, partially for work purposes (widescreen at home is definitely better than the dual-22-inch-1080p setup at work), and partly because bigger works better for my not-as-good-as-they-once-were eyes.
The resolution's a bit much for my aging graphics card, but I can turn down settings, or have the resolution even turned down some, should the need arise. I play somewhat older games, though.
TL;DR - On a technical level, I think you should save up to buy a new MB/CPU/RAM (or just MB/CPU if you get a not-quite-latest-combo that works with DDR3) first. From an eye-comfort level, I'd go with the bigger monitor, knowing that you may need to turn down settings on games to deal with the higher resolution.
EDIT: my son's computer runs a Haswell Pentium G3220 processor, and an R7 250E video card - his video card has a little less power than yours, but he's able to run a number of games at 1080p with medium settings. However, these are somewhat older games. Think Portal 2, Borderlands 2 and Pre-Sequel, etc.