Re Keyboard for 4.5 yr old:
Presumably your child is at school (Reception class?) or in Nursery, or something similar. If so, he/she may well be starting to do some music, at least singing, if not a bit of percussion.
Your request is almost the opposite of what a lot of parents want for their 'musical' child; many seem to want formal lessons, and 'Grades' and ensembles, etc, sometimes TOO EARLY for the child.
You, on the other hand, seem happy for him to 'play around' (which is GREAT) and 'make some noise'. However, I would suggest there is a 'middle path', and at 4 or 5 a child is certainly capable of starting to learn what music is all about, learning to play little tunes, and quite possibly, making up their own tunes.
There are many 'tutor books' available, and a child who is starting to learn to read at school, could be able to follow instructions in a music book equally well. There are also on-line 'lessons' - though some are better than others!
As you mentioned Gumtree, I guess price is an issue, or perhaps you don't want to spend out on something that may not last very long. On the other hand, starting music at a young age can start a child on a lifetime of pleasure and creativity.
My main recommendations would be to have FULL SIZE keys, at least 61 if possible, and not bother with so-called 'teaching features' such as lights that show which note to play. Keyboard is NOT difficult to get started on, and the modern keyboard with several hundred sounds, two hundred accompaniment 'styles', and many other features has its own 'reward system' built in.
Tell me a bit about your child, and I'll look back in a few days.