Once you decide what your system will be then you can phase in the boiler, cylinder etc. Don't just buy a boiler and then think about what you will run off it.
Look at a heat banks, not unvented cylinders.
No problem then, if that is what you want. The existing tank stays. But fit a quick recovery cylinder.
If you went Fortic and a combi, then the existing cold tank can be removed and replaced by the Fortic (assuming enough height in loft), then the airing cupboard is liberated of a space hugging cylinder. Worth thinking about. The Fortic is simple, cheap, space saving and effective, giving a high pressure shower and excellent flow for a bath. There are quick recovery versions of Fortics. See the Range web site. But not cheap.
Indirect combination tank:
You can fit the combi in the airing cupboard and just connect onto the existing system, having the shower off the water section of the combi. Immediate problems solved for now, and then update/remove the cylinder or install a heat bank, etc.
You will not know which way to go until you assess the mains pressure. This may be upgradeable, and if old maybe worth your while doing so.