Howdy bagobats, and welcome to the Guild.
Getting started on a city map can be a bit daunting. They're known to be particularly difficult maps to make, but--in my opinion--very worthwhile and fun, too.
In terms of scale, looking at historic city maps is a good guide. 19th century London is always a good choice for steampunk mappers. London had about 1-1.5 million people. That's not a lot by today's standards, but it was huge back then. Of course, in a fantasy world you can make it as big or as small as you want, but remember, the inhabitants of your city will still need sufficient food, water, building materials, etc.
Physically, London may have been about 6-7 miles wide (~9.5-11km) and about 3.5 miles high (~5.5km). These are **extremely** approximate figures based on historic maps, but give an approximate sense of size, nonetheless... I'm glad to see you want to keep your buildings quite densely packed. It makes for a much more realistic city map, I think.
In terms of planning your streets, I think the first thing you should do is work out your topography, and draw a simple map (which can be for your own reference only) showing major features like rivers, hills, swamps, farmland etc. It can also be a good idea, I think, to decide at that point whereabouts your city first began to develop, as that will most likely still be the centre of the city today.
Next, try placing some major landmarks: the palace, markets, docks, castle, cathedral etc. Once you have these, you can start drawing lines connecting them, which will become your first major roads. Adding more roads that lead off the map to towns/cities near and far is also a good way to put down some major roads. Giving the lines a gentle curving look will help make them realistic: major roads aren't likely to be weaving all over the place, but nor are they going to be dead straight.
With major roads and topography started (and you can do that in 1-3 hours, usually), you're well on your way to making a city map. One piece of advice I can't recommend highly enough is to post a work in progress here on the guild: the feedback and support you'll get is always excellent.
Hope some of that is helpful.
THW