Good type of bike to get for commuting (thinking of road v touring) I'm new to this site but I've been intrigued by the thought of picking up cycling as a means of my new way of transport as well as for recreational purposes. 

As a little background, I live in London and as a recent graduate, I do not have the widest of budgets but I would not mind spending at most £1000 for a bike (thank you cycle to work scheme.) I weigh around 63kg and I am a bit of a tiny man sizing up to around 165cm.

I had previously owned a mountain bike when I was younger, but I had recently purchased a second hand road bike for £60, which I have found an absolute joy to ride! My stamina/endurance isn't at the greatest yet, so I plan to stick with my road bike to practice and build up stamina, but I really want to find what might be the best bike for me in the long run. I do know that touring bikes would be great, especially since it can handle extra loads, which would be brilliant for shopping. But I am worried that the extra weight due to being a steel frame would highly impact my speed in the long run. 

My current milestone goal is to be able to start cycling to work, though considering it's winter right now, I am aiming for this at around spring/summer. The reason I think the weight might come to play is because I will be traveling around 13 miles one way. Thus, if someone could enlighten me if the weight of a touring would heavily hamper my journey, I'd really appreciate it!

I digressed quite a bit but, in short if anyone could give me some advice on what would be a good choice of bike for commuting for me with drop handlebars (I've fallen in love with this form) I would really appreciate any of the expertise you can provide me!

If I haven't provided enough information, please just give me a shout and I'll get back as quick as I can.
There are a bunch of bikes sold in the UK that are specifically designed for the cycle-to-work scheme: they have good specs for commuting, are priced to come in under the £1000 limit, etc. A number of online vendors stock these. So that would be a good place to start. Or find someone selling one of those bikes used.

The additional weight of a steel bike is not that significant. Less than 1 kg. When you get done fitting mudguards, racks, lights, a toolkit, and whatever you're schlepping to work, you won't really notice the difference. That said, as Argenti points out, you'll probably be shopping for either steel or aluminum. They're both good options.

Also budget for the clothing and accessories you'll need to ride comfortably and safely. That would be a subject for another post entirely.