I first moved to Berlin with nothing - small suitcase, minimal German and high hopes.
You are doing everything correctly.
Whenever moving to a new country, be sure to have enough money to live comfortably for at least 3 months (which you have) without working.
The first thing you should do would be find a cafe/bar and go there on a regular basis. Eventually you start to see and meet the same people. Then you can slowly begin to network and slowly spread the word you are here to stay and looking for work.
I don’t care if everyone speaks English, it is mandatory that you at least try to learn some Swedish - learning the local language is a huge plus; it shows you care enough to learn and are there for the long haul.
The old adage “best place to learn a language is in bed” is true. Should you get that job as towel boy for the Swedish soccer team, spend a few months with Sven under the covers and your Swedish will improve greatly and quickly.
As I mentioned in a recent thread about Sweden, after observing that everyone in that country is drop-dead gorgeous, a friend suggested “perhaps they kill ugly babies at birth”, so be prepared to ogle and drool a lot there.
My only quibble with moving to Sweden would be the weather and the long seasons of days or nights…I’m too old for the cold now, give me warm climate any day!
But other than that - wonderful country, wonderful people and you will, ahem, “have a ball”.
Keep us posted on this great new adventure!
As our goals do not conflict, I wish you the best of luck!
Thanks DMark - that’s all encouraging.
Yes I have money as you recommend, and I’ve been studying Swedish for nearly two years so I can converse simply in it. I suspect after being there for a couple of months I’ll be near fluent, I just need continual exposure to bring what I have together. Plus anyone who emigrates to Sweden can enrol in free Swedish lessons provided by the state, and you know I’ll be doing that.
I like the suggestion of hanging out in a cafe/bar on a regular basis, I think that’s a good idea! Buy the paper, hang out, meet people, not a bad idea at all. As for spending time under the covers with Sven, I’m totally not averse to this plan 
I lived in Sweden for a month last year, and have been there enough times to be fully aware of how stunning everyone is. I think I’m at the point where I shouldn’t wander around with my mouth open now 
I’m prepared for the weather, at least I think I am. I’ve visited Sweden in all seasons but I guess I’ll find out what it’s like to live there. The UK isn’t a million miles away in terms of climate and variability of days in the seasons, and I’m moving to Gothenburg which is in the relative south of the country so the changes won’t be too extreme.