as your needs are pretty basic you could consider a refurbised Mini , but ...(there is always a but somewhere 😕)
despite you got monitor and keyboard and mouse already ,and not that you would really have the need for a better monitor and keyboard , i would look to get a refurbished iMac 21.5 , it offers just more value for the money , but keep your mouse for a while ,as the magic mouse that comes with a iMac is not to everyones taste 😉