Hi Lucy
I'd say it's very much down to personal choice whether you keep them in a run or totally free-ranging, it would also depend on the location too.
Ours are in a large run as we live on a busy-ish road, and I don't want them roaming into our neighbours' gardens or the local school grounds (with is just up the road from us). If our garden was more secure I'd be tempted to leave them totally free-range; do you own the fields next to your garden -- would it be a problem if they strayed onto that land?
A run would probably be a good idea if you don't want your two year old walking in their poo, it's just a fenced off area of the garden so that doesn't cost much - just chicken wire (or fox-proof stuff) and fencing posts.
If you are anyway 'handy' you could convert a shed to make your own henhouse, or Wildeone on here is thinking about converting a rabbit hutch.
I do hope that you go ahead with getting hens, you really won't regret it and it will really enrich your life. Your two year old will love them too
I hope some of that is of some help