Small organisations, like any others, must keep accounts. This is invariably done by people with little or no accounting experience - often a reluctant volunteer or staff member.
In these situations, routines and simple procedures are important, and a cash-based system is probably best. You enter payments as you make them, allocate them to an account such as 'telephone' or 'grants', and produce nice, simple reports.
Sometimes, though, an organisation hires accountants: they decide that what's needed is an 'accruals' system, whereby you enter things that should have happened, even if they haven't. Imagine it's the end of March and you haven't paid the tax bill yet. On a cash-based system, all you do is tell your trustees in a note that you owe the tax. On an accruals system, however, you can do what's called a journal.
Your reports will then show that you have incurred this expense, and your 'balance sheet' will show that the money remains in your bank, but you still owe the tax. In April, when the bill, is paid, you effectively reverse this journal. You will soon have journals for all sorts of things - prepayments, depreciation of fixed assets and so on.
And then the accountant leaves and it's back to the reluctant volunteer. I guarantee that this will end in tears. Accrual accounts are useful and informative, but much more difficult. You need to think long term. Will you always have staff or volunteers who can handle this? Maybe you should just keep it simple.