If you hold your shares in an ISA, which for tax reasons is probably the most advantageous way to hold a portfolio up to the annual contribution limit, then these will have to be in a nominee account as there is no choice.
CREST applies only to direct holdings outside an ISA and is a compromise between being on the share register and permitting electronic trading. But it costs. Only a few brokers offer personal CREST accounts and there is a regular charge involved. So in practice CREST is really only worthwhile for larger portfolios.
For direct holdings apart from CREST there are two options, nominee accounts or paper certificates. Paper is quite rare these days and does not allow for electronic trading, but it does put your name on the share register. Paper though attracts higher dealing charges than nominee accounts. The advantage of the latter is low charges and electronic trading, but there is the very slight risk of failure of the nominee company and the holder’s name is not on the share register. Investors should be covered to a large extent by compensation schemes but the problem is that it would take ages to sort out and you may not recover all your investment value in the event of failure. Despte this very slight risk, I’d guess that the great majority of small private investors use nominee accounts these days.
It’s your choice, outside of an ISA, which holding method you select.