Hello! Self-employed sole trader here who does all her own taxes. Mine are pretty simple and your husband's should be too. I can't speak for rental income.
When you come to fill in the form, in essence it is as simple as adding up all your income, adding up all your expenses, and then the form does the calculations and tells you how much to pay.
For income records, I keep all my invoices in one folder on my computer along with a spreadsheet with a running total. End of the year, I print them out and stick them in a ringbinder.
For expenses, I keep an envelope in my desk. Physical receipts go in there with a brief note about what it was (because you WILL forget!). I only have about half a dozen a year. I have a label in my gmail inbox for email receipts. Again, I don't have many. You can only claim back unreimbursed expenses and most of mine are reimbursed. I also don't bother with calculating percentages of my internet bill and the like because I rarely pay much if any tax anyway.
The rule of thumb I was given was to put aside 25% of income because it's basic rate tax plus national insurance. However, the personal allowance means that 20% will probably be sufficient if he's not earning a lot of money. I'd do 25% the first year and see how it goes, though - worst case scenario you end up with a bit left over to go into investments!
DO YOUR TAXES EARLY. You get until 31st January if you do them online but DO NOT LEAVE IT THIS LATE. You might forget, your computer might break, and HMRC will be clogged up by everyone else panic-doing their taxes. I do mine around the summer solstice - long enough for any last bits of money to come through but early enough for serious peace of mind. He should register as self-employed ASAP, though, because he will need to set up an online account which involves being sent stuff through the post.
HMRC are super duper nice if you ring them up with questions. Just explain its your first time doing your taxes and they will help. But it's really not difficult - a lot of the form is ticking "No, this incredibly specific situation does not apply to me". And as a writer he's unlikely to have complicated expense scenarios.