If you want to keep it for long term, then better get a new one, 1 year official warranty, 100% original with peace of mind. Price is going to lower in few days. P8 Lite, Honor 4C, Y6 Pro, Lenovo K3 note, Lenovo A6010, Vibe P1M, you can get upto 11% off at their company price. Try hyperstar. They are all within 14500-18000/- brand new. Perfect for day to day tasks (no hanging issues) and P8 Lite and Honor 4C have very good cameras. Perfect for those who want to get things done on smartphone, rather than showing off (that too with old and outdated beaten up flagships)
S4 is mostly 12-13 these days, so rate is good, as its value edition model, launched one year after original S4. But to be honest, there is a lot of garbage in market these days, especially with 2013/2014 models, so you need to be skilled enough.
I remember that you have mischievous kids, so keep repairing stuff in consideration. S4 front broken glass replacement usually costs 2500/- (for good quality) and full LCD panel costs 5000-7500 (for new A+ copy). It is not water resistant.
Lenovo phones have splash-proof nano coating (slight water resistance), so if liquids fall on it, nothing bad happens. You can dunk Lenovo phones in water and take it out 5 times a day and nothing bad happens. But they cannot be submerged in water for too long. Their LCD replacement from service centre is expensive (due to nano coating) 5000-7500/-, but you can get from market at 1/2 to 1/3 costs of service centre (but non original may not be nano coated).
Huawei is not water resistant, but its repairing is very economical. Like, P8 Lite LCD replacement is ~3000/- from market and 6500/- from service centre. Used Y6 Pro comes with accidental coverage in your budget. No idea about if Huawei accidental coverage is legit or not.
So do check atleast LCD replacement costs before final consideration.
Sorry, long rant xD, as my typing speed is super fast.