1. The selection of size should be matched to resolution. It's all about pixel density or pixels per inch (ppi). The human eye can start to "see" individual pixles at about 96 ppi and this number was part of the reason why Windows OS was designed around 96 ppi and the reason most monitors are in a certain size range
At 1080p, a 23" screen has 95.8 ppi
At 1440p, a 27" screen has 108.8 ppi
Now if you put 1920 x 1080 pixels on a 27" screen, you are down to a pixel density of just 81.6 and the average person with "normal" vision will be able to see individual pixels at typical viewing distances. And this will make the image appear grainy
You're going the other way squeezing 1440ps worth of pixles into a 22" screen which results in 133.5. While certainly doable, I have see 4k screens on 17" laptops, its going to be quite hard to see the difference. In short, you will be paying more, for an advantage that your eyes are not really capable of seeing.
Here's the PCpartpicker link for all the 1440p monitors they track.
https://pcpartpicker.com/products/monitor/#r=256001440&sort=size&page=1
2. As to refresh rate, there are many 144+ Hz monitors at 1080p, the most popular of which is the Asus VG248QE. It has the added bonus of being able to use Motion Blur Reduction via the toastystrobelight utility
3. As to quality IPS / VA the IPS panels that are available at 1080P are priced such that for only a few more bucks you can get a 27" 1440p screen; this makes them very hard to recommend.
You just can't ;look at a TN screen and an IPS screen and make conclusive judgements about the technology, quality varies in a big way between panels.
While it is certainly true that the best IPS panels are better than the best TN panels, if given the choice between a $300 IPS panel and a $300 TN panel, if the usage includes gaming, the IPS just won't cut it.
The quality IPS monitors with panels suitable for gaming are made by AU Optronics are up near $600 (1080p). With the 1440p models at $700, it's hard to make a case for 1080p.
You should also take into account what GFX card will be driving the monitor.
Freesync monitors cater to the technology in AMD GFX cards and it has a primary range range from 40 - 60 fps. There are still advantages to be gained above 60, but the level of improvement to be gained diminishes the higher it goes.
G-sync monitors cater to the technology in AMD GFX cards and it has a primary range range from 30 - 60 fps. There are still advantages to be gained above 60, but again the level of improvement to be gained diminishes the higher it goes. How G-Sync differs is in that it contains a hardware module which provides for ULMB, a Motion Blue reduction technology.
This technology strobes the backlight to eliminate ghosting. If you visit the blurbusters site, you can see how this technology works by looking at the 1st three photographs here:
https://www.youtube.com/watch?v=hD5gjAs1A2s
The blur is obvious but once the MBR reduction technology is turned on, it all but disappears.
http://www.blurbusters.com/faq/60vs120vslb/
Some Freesync monitors have proprietary hardware modules for MBR included but the quality and effectiveness varies between manufacturers and models.