5.1 Natural or synthetic?

5.1.1 Natural

Natural seawater has much to recommend it. It is 'alive', which can have positive effects for filter feeding organisms, has the right balance of chemical substances in it, and is free.
BUT, assuming you don't live 20 metres from the next coral reef, things may be different.
You may have noticed (live or on film) that the seas where our creatures come from are bluish in colour. Although reefs seem to be teeming with life, they are local oases in what is really a watery desert. The waters of the North Sea and North Atlantic are green. The colour is due to the much higher levels of nutrients and plancton in these waters. Although nutrients may not present a problem, this isn't true if you collect anywhere near sewage outfalls, rivers, or beaches where cows might be grazing.This presents a possible problem for the aquarist. So collect well out to sea or at least from an isolated rocky coast. Transport the water any distance, or heat it, the dead planctonic life may be a considerable source of pollution. There may also be the small chance of disease, but this is negligible in comparison to adding a new animal to your collection.

5.1.2 Synthetic

Synthetic seawater is made by taking a ready- mixed bag of aquarium salt crystals and dissolving it in water. Using brand named salt mixes will ensure a good quality. One product is made by evaporating clean seawater and selling the resulting crystals. Otherwise, these mixes are made up of single component salts of high quality (the manufacturers usually talk of 'analytical' grade, which means the individual substances are pretty well as pure as the chemical industry can get them).
The word 'salt' defines a particular type of chemical substance of which 'common salt' is just one.
Most of these salt mixes, when made up with reverse osmosis water, create a seawater which is not identical with natural seawater.

5.2 Filtration:

or how we get the crud out! Mainly food remains and fish faeces. The nideal system, which may be comprised of more than one component does this: NH3/NH4+ > NO2+ > NO3+ then NO3+ > N2
There is no bacterial way to remove phosphate- this needs either algae or a chemical means.
Adding calcium hydroxide to raise calcium levels may well precipitate solid calcium phosphate, but there is always a small chance this can reverse under unfavourable circumstances. Proprietary removers are better (e.g. Rowaphos, or others)

Berlin system- use of live rock and skimmer (usually in filter sump). Live rock has aerobic and anoxic reductive areas to convert any waste nitrate to nitrogen.
Jaubert system- use of a 'plenum'- a depth of 10cm or so broken coral or coral sand either directly in the aquarium or in the sump. This lies on a perforated plate fixed 1cm or so above the tank base. Small creatures encouraged to burrow in the top layer. Milieu changes with depth from aerobic to reductive. Layer depth a problem in a small tank
Algae filter- will remove nitrate and phosphate when you harvest the algae
Sulphur filter- must be combined with calcium carbonate to remove sulphuric acid. Can disturb calcium/ alkalinity balance.
Miracle Mud filter- seems to work very well in a sump, no personal experience

Filters that don't do the business in marine reef setups: trickle filters, undergravel filters.