Hm.. Before i answer this i would like to point out that if yu head down the route of the cheapest option for your marine takn then you are going to run into trouble at some point in the future. Whilst i am not saying that running a marine tank on the cheapest budget you can manage is no feasable, it does usually mean that should things go wrong then you have less of a margin for recovery.
As for filtration... This is something i simply would not shortcut, there is only 1 major form of filtration and this is liverock. Its the best you can have and its definately not cheap. Should you opt for mechanical filtration like a cannister filter then you will be make more frequent and larger water cahnges which over time will cost you much much more than the liverock. Undergravel filtration is ok and i would still use it for fish only systems but its still no match for liverock.
Liverock is really your only main source of filtration, you can of course suppliment this with othr methods should you choose and these can be done cheaply (or expensive as your budget dictates), DSB, Mineral Mud systems, Denitrificators, mechanical externals, Skimmers, Ozone, UV and many other methods. These all work with liverock and have varying degrees of success.
Some people dont like the price of liverock but they still have to fork out hard earned cash for some other filtration method AND of course some sort of rocks etc for aquascaping, why not just get liverock and it does both in 1 purchase.