If I buy a router will my internet be faster?

[I chose best answer]

my internet is ok but I want it to be faster and I'm wondering if I replace the router my dad has with a stronger one will me internet be faster?
theres also this black thing that is connected to the router that i think is called a moden and if i buy a better moden will my internet be faster too? i have like 200 dollars right now and i already bought everything i wnt so i wnt to get myself faster internet now
well how do i know if my dad bought a modern router?
i think the one we have sux and is making the internet speed our provider is giving us a bit slower than it should be

also wont a new router give a better wireless signal because i use my phone a lot and if im upstairs it sometimes lags because my router is downstairs