..I thought about an old-fashioned hand-push one as I have always enjoyed using my dad's...
Today's push mowers are not actually like the 'old-fashioned' mowers. Today's push mowers are light-weight and are much easier to push.
I would not consider using anything but a push mower. They are easier to use than petrol or electric mowers. There is no fuss, no mess, and no running cost.
The Qualcast Panthers are still in production. The 30 and 38 model numbers refer to the blade width in cms. The 38cm one is better for people who have a medium to large size lawn.
The very same mower is marketed under a number of other brand names too. The Bosch Panther (mentioned in message 2) is exactly the same mower. The Qualcast and Bosch Panthers are made at the same factory in China.
Also worth mentioning is the Webb 12" push mower. This is a new model, introduced in March this year. It's a bit more expensive than the Panthers. The Webb has a rear roller (message 4) to give stripes, and it has a more substantial grass box.
There is also a high-tech push mower made by Brill. The Brill RazorCut is made in Germany and is 'Vorsprung Durch Technik' (Progress Through Technology). This is the future of grass-cutting. The Brill is not available at garden centres but is available through Amazon. The Brill is considerably more expensive than the others, but worth it, for those who like to stay a few steps ahead of Jeremy Clarkson.
But if you just want the grass cut, then you can't do better than a Qualcast (or Bosch) Panther.