I recommend a Rhode Gear Taxi seat which comes complete with lightweight Blackburn rack and retails for around £79. Once clipped into the rack, the seat is as solid as if it was part of the frame. Make sure you get the seat with adjustable back, though, so your child can slumber in comfort without getting a crooked neck.
An alternative to a child seat is a trailer which is an enclosed, tent-like carrier with sides that roll up and a flag on the top for visibility. While substantial in size they are relatively light as they’re made from aluminium and very safe. On the downside they’re very expensive to buy and, since the child is sitting only just above ground level, he sees very little of the passing scenery so has little sensation of cycling.
Tag-a-long bikes for children attach via a moveable bracket to the seat post of the adult bike and consist of a single, rear wheel. The front wheel of the tag-a-long is effectively the back wheel of the adult bike. They are a great way of ensuring the safety of your child but also being able to cover a reasonable amount of ground too. Cycling with the additional load can be hard work for the adult especially going uphill and as the child gets older.
An interesting variant of the tag-a-long is the Trail Gator. This is a stem which connects a normal, two-wheeled child’s bike to the seat post of the adult bike. The big advantage is that you can uncouple the bikes to ride solo part of the time if you like. Trail Gators don’t fit all bikes so check carefully before you buy.
Soon enough your child will be able to cycle solo, of course. But if you want to increase their range then consider a tandem if only to hire. My son was safe on a tandem with the saddle at its lowest height from the age of 11. They are great fun, the chief advantage being that the adult (pilot) can over-compensate for the child (stoker). But keep checking to make sure that s/he is still turning the pedals! Also don’t dismount in the usual way as you will may kick your passenger in the face.