you can use a combi boiler to heat an unvented cylinder if for some reason you want to, for example if you already have one. A conventional boiler will be less complex and have less to go wrong. Modern boilers are (almost) exclusively all condensing so are all very efficient.
Poor flow (not pressure) from your old taps is probably because they are fed from old half-inch or 15mm pipes. To get the best flow out of your new supply pipe, the stop-cocks and service valves, especially, need to be changed to full-bore ones, and from the incoming stopcock you should run a short piece of 28mm copper or 32mm plastic, connected to which are a 22mm pipe to your unvented cylinder, and another 22mm pipe for your cold supply, with the individual pipes tee'd off it. Bath taps should be fed in 22mm pipe. By supplying each of the users from a larger supply, you can turn on any of the loads and the supply will still be big enough to feed the other users.
Each pipe size has about twice the capacity of the next size down (28mm, 22mm, 15mm) so you can feed two of the smaller pipes from it and still get good flow. However, if you tried to feed two 15mm pipes from one 15mm supply, the flow would be roughly halved for each of them.
Look for full bore valves made by Pegler. If you look inside them and compare them with common cheap ones you will see they do not constrict the flow.
Any of your taps fed from a cold-water tank in the loft will have low pressure.