additionally your dad’s speakers may sound quite differently than today studio monitors.
i have a friend bought 20 or more year old B&W which have too much high’s overall and while it may be perfectly suited for vinyls for todays CDs it is too much highs.
they manufactured hi-end speakers different at that time.
additionally, you might want to consider picking active monitors (more expensive with built in amplifier) so that you don’t have to care about adjusting cables + amplifier + monitors to get more even frequency response curve.
but you are looking for cheaper solution: i suggest small HI-FI speakers from well known manufacturers like JBL, B&W, Infinity etc. You can learn about their quality by reading reviews in hi-fi magazines and eventually you’ll be able to choose one.
you need those with flattest possible frequency response curve (nowadays this curve is drawn only for studio speakers) usually you’ll encounter values like “frequency response 20-20000 Hz, +/- 3db”. Studio monitors have +/- 1,5 db, normal hifi speakers have something like 3db.
completely other thing is speaker placement: they need to be somewhere in height where your ears are - you need to sit in the center (better studio monitors have this sitting point quite dispersed while lousier ones - you need to sit at exactly one point to get perfect sound).
moving speakers closer to walls will increase bass, moving them away will decrease it, moving it lower will increase bass, moving it upper will increase highs… etc…etc.
on high end studio monitors you even have a setting to emulate normal speakers and also setting for adjusting sound, relative to speaker placement in the room (it is not the same if they are in the center of room and you have some space in front and behind them, on the room edges, just before wall in front of you…)
as a final word, you can achieve quite decent quality with hifi speakers (not the ones from mini-systems) but for final production some studio reference will be probably needed. and always target your music to sound better on speakers rather than headhones. more people listen on speakers