Sometimes I like to use logic to answer some questions.
If you can't afford a 144 hz monitor, it is unlikely that you have built a computer capable of playing games at that refresh rate. And since you are asking about an "older" monitor, I assume that you didn't build your own PC by meticulously researching every component, so a "good" monitor you can afford will be just fine.
I concur with SkyNetRising when they recommend a 1920 x 1080 monitor of less than 27". And feelingfroggy777 offers good information.
1080 because that is "HD". Check out any article on resolution to understand that specification. If you are watching "TV" on your monitor then 1080 is important. And that should be the "native" resolution.
Under 27" because at typical desktop viewing distances anything 27" and larger it "too" big. You will be able to notice all sorts of "flaws" in the image.
The "sweet spot" in monitors right now is the 23" to 24" size. You should be able to find many highly rated ones for well under $100.
I may be wrong with my initial analysis of your PC's capabilities, but most gamers would advise putting money into the graphics card to boost your frame rates rather than the monitor. On the other hand, if your monitor is "ugly" then you are not going to enjoy the visual aspects of the game.
Buy a monitor that will display a pleasing picture within your budget. The sit back and enjoy.