We can't decide what kind of reading glasses you need by the number 20/40 cuz we can't change it to a prescription required in corrective glasses. You will need a more specified prescription to decide what number you need .
According to your description, your vision is lower than average vision. Usually, 20/20 vision stands for the average vision. The lady there said you have 20/40 Reading glasses, that is to say you need Reading glasses with +0.75 prescription. But personally, your vision is not so bad. You actually needn't reading glasses if you not do too much near vision related work.