Sajom5271

I have owned the G203 (Identical to the G102 just sold in different regions) And I highly recommend it, it has held up really well and I have never had any spinnout/tracking issues in fps games. It is a tad bit on the small size but my hands are similarly sized to yours and i aim very well with it. 
 
I have used the G402 but it was to large for my liking and since it is getting closer in price to the FK1 then i would save up and buy that. 
 
I have never used the Rival 110 but I have heard great things about it. 

I'd say since you mostly play FPSs, as long as you don't use a palm grip, the G102 is probably the best option out of these 3.
 
The FK1/2 and the G403/305 are also really good, if you prefer the shape or want wireless (G305)

How about an AM4 motherboard (even an A320 based board which won't allow overclocking) with an Athlon 200GE processor (dual core ryzen with integrated graphics)
Should be as fast as that Pentium or faster, and you can actually play games at 720p or such resolutions with the integrated graphics, so you could put the money for the graphics card aside and get more money and then buy a RX 570
 
Also one other thing to mention : these modern video cards like GTX 1050 or RX 560 don't have analogue outputs (vga), so make sure your monitor has at least one digital connection (dvi, hdmi, etc). IF your monitor has only VGA, you would need to buy an active hdmi to vga converter, or - if you can buy an AM4 board and you would be willing to use integrated graphics, there are a few that have vga on them, besides hdmi and/or dvi.
 
 

Sadly you're in Bangladesh, otherwise I would tell you to get a RX 570.
 
I think GTX 1050ti is a bit faster than RX 560 and you can always buy a second stick of DDR4 to have 8 GB in total at a later time.