Type of tank - depends on many factors. Will it supply 2 showers, 2 sinks, and 2 basins - yes if it's sized correctly.
Now, types of tank available ...
There's the traditional open vented cylinder. Pros: cheap, well understood. Cons: Need potentially large header tank, very low pressure (only whatever head there is from water level in header tank to outlet, so barely anything in most flats). Pressure can be boosted with a pump - but that makes your shower very noisy
Unvented cylinder. Pros: gives you mains pressure hot water. Cons: Expensive, dangerous enough that the regs require they be fitted by a suitably qualified plumber and they must be a complete package of cylinder and the multiple safety devices, have restrictions on where the safety vent pipe can be run which restrict their siting in many properties.
Also consider:
Thermal store or heatbank. Pros: gives you mains pressure hot water, cylinder itself is open vented and doesn't need the safety systems of an unvented system, can DIY fit, can DIY a heat bank if you're that way inclined, if suitably sized can be used to run wet central heating (and you can use a modulating pump for an efficient and virtually silent system). Cons: Many plumbers are ignorant of them (I've even read some comments from them that they would never ever suggest one which means they would willingly mislead some customers
), can be expensive (depending on type), may struggle finding a local plumber who doesn't do the tradesman's special "sucking through teeth" before telling you it needs ripping out and replacing with his preferred solution (usually a combi), may need electrical power to have hot water.
At one point, thermal store generally meant a passive type needing no electrical power (the heat exchanger being a large coil inside the cylinder, working a bit like the reheat coil in a traditional DHW cylinder but in reverse), and heat bank meant a cylinder where the heat exchanger (typically a plate heat exchanger) is external and a pump circulates water from the cylinder through the PHE as required. However, these days it seems that the distinction has disappeared and both types are just called thermal stores.
Both types have their pros and cons, but either would do for you - provided it's sized correctly.
The key thing is correct sizing. In theory you can't go too big, all it would do is take longer to heat up, but would otherwise allow you hot water usage that you aren't needing - but of course, the larger it is, the more space it takes up and the higher the floor loading (which is always something to consider).
But if undersized, you risk running out of hot water if everyone wants baths and showers at similar times.
If you did decide to use wet CH with a thermal store, then you do need a significantly larger store, but you could (in theory) take advantage of any multi-rate tariffs available (eg the old E7). I say "in theory" because it seems the saving on "cheap rate" has diminished significantly in recent years - I imagine due to a combination of there being less nuclear (works best if run at full, or at least constant, output all the time) and the population being more varied in their lifestyles. But it's not hard to arrange the store to fully heat everything on a cheap rate, but only top up part of the store as needed the rest of the time.
At some point I think we can expect tariffs designed for this sort of thing, where they can remotely control your immersion heater(s) (as a means of demand management, with certain availability guarantees) in return for lower rates. But AFAIK we don't have those yet - and the protocols for smart metering don't support them as they'd need to be done.
