Without you having already gotten the water tested, what makes you think it isn't safe to drink already? It's only brown, that's sediment or rust discoloration. Unappealing but not actually bad for you.
Filtration will reduce the suspended contaminants and certain, more comprehensive filters can reduce other, dissolved contaminants. But for the water to be absolutely clean you would need a reverse osmosis or distillation system, which is expensive and requires power to operate.
Get the water tested. If it comes up unsafe, you actually can then compel the landlord to repair the piping and you won't need a filtration system.