Well, I'm an unschooler and my kids didn't do GCSEs at the usual age in the usual way, so I can't speak from experience. However, the subject is much discussed and I have spent huge amounts of time around other parents HEing teens, so I can give you some tips.
Online school is possible but is not the most popular way to prepare for GCSEs. I don't think most of them do organise exams for you, but maybe someone can correct me if they know of a school which does do all that. A few disreputable online schools have even been known to sell courses preparing kids for exams which they know full well the parents will struggle to arrange!!! Most people use a more flexible "pick and mix" sort of approach in which they choose whichever resources work best for their child on a per-subject basis. So for example, maths is a straightforward subject for which a mathematically talented kid probably wouldn't need a tutor, and such a child might just use books and online resources to teach themselves. Maybe they want a more sociable environment to learn German, so they go to an in-person local tutor group arranged by another parent. If they find essay-writing a big challenge, they might use a one-to-one tutor for it. And so on. Often people just look around to see what's on offer and if something looks appealing they go for it. Maybe there is a particular subject which they weren't necessarily planning to do but they absolutely love how it is taught by a local tutor, so they choose it. Some colleges have 14-16 programmes at which your child may be able to do a few GCSEs now, or do a set of "catch-up" GCSEs at 16 if they aren't ready now.
Most home educators spread exams over several years rather than doing them all in one sitting, usually starting with the child's strongest subject or one which they consider relatively straightforward to answer - so it is more common to do maths early than English Language. Spreading them out reduces stress and allows the child to focus on just a few subjects at a time rather than juggling many, as well as allowing them to learn from their previous exam experiences and feel more relaxed in subsequent exams.
I'd suggest making contact with your local home ed group. People there will be able to tell you about local opportunities such as college courses, in-person study groups, and recommended one-to-one tutors. Also, you'll be able to find out about social opportunities for your kids.