Then I suggest you go ahead with an Asus branded router. I am using Asus N66U for the last 6 years. It is a triple antennae router and there have been no issues with the number of devices. At any point in time, I have my tv, mobile, office laptop, personal desktop, echo dot, firestick, and a few smart bulbs. I have friends coming over and even when they connect their mobiles there is no lag of any kind.
But Asus branded routers will be above your budget. TP-Link, Tenda also gives high-performance routers at a cheap price but not sure about their performance. D-Link should be a better option performance-wise but not that particular model which I quoted above. You gonna have to do some online research on the router models in your budget, I am sure you will find one. Another option is the Mi Router, it has 4 antennae and fits in your budget. You will also find tons of reviews for it online.