The VG248QE is old but relatively cheap, so it's a good starter option. 240Hz availability is tough in some countries.
Refresh rate is more important than 1ms of extra latency for many esports. The reduced sampling/scanout latency can sometimes outweigh absolute latency. A 240Hz display can refresh in 1/240sec even at 144fps. See
High Speed Video of LCD Refreshing.
For example, the first 25ms of refresh cycles, the sampling (scanout completion) lantency:
120Hz: T+0ms, 8ms, 16ms, 24ms
240Hz: T+0ms,
4ms, 8ms,
12ms, 16ms
20ms, 24ms
Now if you add 1ms absolute latency (tape delay) to the 240Hz monitor:
120Hz: T+0ms, 8ms, 16ms, 24ms
240Hz: T+1ms,
5ms, 9ms,
13ms, 17ms
21ms, 25ms
You notice that the extra samples of extra refresh cycles (5ms, 13ms, 21ms) is still less than the 120Hz monitor of 8ms, 16ms, 24ms. Latency is not a single number.
In addition, 240Hz has half the motion blur of 120Hz, since doubling refresh rate halves scrolling motion blur. This is great for things like web browser scrolling and such.
All things equal (GtG lag + processing lag):
144fps at 240Hz has less tearing than 144fps at 144Hz.
144fps at 240Hz has less lag than 144fps at 144Hz
However, a cheap 240Hz monitor can have worse ghosting than a very good 144Hz monitor, so there's an element of panel quality that can make 240hz worse. However, most will get better esports with 240Hz+. On the other hand, I understand availability/price options are often extremely limited and going with 144Hz is easier/more affordable in many countries.