I would recommend that you take a look at getting an Electra Townie bike. They use what they call 'flat foot technology', which is where you can put your feet down on the ground easily and without having to hop off the saddle or balance the bike on a tip-toe. They achieve this by putting the bars higher, the pedals further forward and the seat back. This works well in flat terrain but is not so good out of the saddle going up e.g. Cotswold hills. But you aren't going to be doing that with a childseat on the back, so have a look into it.
Regardless of whether you are male or female, a step through frame is a very good idea when carrying a child seat. Step-thru frames are definitely not just for girls, the benefit is getting on or off and not having to swing a leg over the front or the back of the bike.
Carrying stuff with a bike that has a child on the back is not that simple, you don't want a rucksack and panniers are not going to happen. A basket is what you want, ideally one that is bolted to the frame and not the handlebars. In that way the steering is not affected.
Weight doesn't make any difference to a bike if you are loading it up with a heavy child on the back. Riding is a momentum thing. Take a look at the Kona Africabike - this has three speeds, possibly a back-pedal brake, 'Northroad' style handlebars, chunky bullet-proof tyres, step-through frame, basket correctly mounted on the front, a rack on the back and a built in lock that should be enough for a two-minute stop to get a pint of milk. The Africabike scheme is definitely something you will want to be part of - for every two bikes sold in the West one is donated to some doctor/midwife person in Africa. The older ones are made of steel and very heavy, plus they have a rack that is too wide for a child seat. The newer 2011 ones in white are alloy with a narrow rack that does take a child seat. The rack is a lot more solid than regular racks as it is part of the frame. This will impact your choice of child-seat, you may want to go for a Hamax one as they have built in suspension. There is also a sturdy kick-stand on the Africabike, useful for when loading up the bike and not having that many hands free.
As for the back-pedal brake, it is very useful if you have a dog on a lead with you!
Another option is to go retro. A 1950's Raleigh 3-Speed will have most of the benefits of the 'expensive' Electra bikes. There are still plenty of them to be had in good condition, complete with mudguards and hub dynamo. These have the relaxed riding position and are incredibly stable compared to today's 'twitchy' bikes. The bottom bracket is lower, the seat typically has big and comfy springs in it and the handlebars are the wrap-around 'Northroad' sort. You can easily put your foot down when stopped and not have to get off the seat. Ladies versions are around although they do flex more than the gent's versions. So long as you have got the childseat on the back, ladies frame is what you want and it doesn't look silly if you are not a lady.
You may also want to check out what the Dutch and Danish cyclists use to ferry their kids about with if those pointers don't bear fruit.
Hope that helps!