Hi OP, this must be such a shock for you I can only imagine how you are feeling at the moment. I am a single parent and am a part of various single parent networks so I thought i would give my perspective and opinions- sorry its so long!
The first step is definitely the DNA test. Assuming that comes back positive, and there are no other surprises, the first and most important thing to do is to start setting out a good relationship with the mother. If, as you are saying, you do want your husbands daughter to be a part of your family, discussions about contact are as important as the discussions about finances (and from the child's perspective are more important as this is a massive change in her life) and so need to be raised straight away.
Thinking about finances first though, becasue that is relatively straightforward. Most people come to a financial agreement between themselves. You should try to do this if possible, and make sure you make the payments reguarly, as if you end up with an agreement through the CMS they take a significant chunk of the money to cover their admin fees, which benefits neither you or your stepdaughter. I realise this will be harder becasue you dont have any relationship with the mother yet, and her first actions have been quite aggressive, which is why I say the first thing to do is to establish a positive relationship with her. When people make their financial agreement between themselves this can be for any amount- more or less than the figures on the website you saw. With the distance between where you live you should agree how transport costs are paid to facilitate contact as a part of the financial settlement. Just a suggestion- the mother may be contacting you now because they have some sort of financial difficulty- a big reason why people don't ask a father for maintanance is because they would rather do without the money than deal with contact/have someone else with parental responsibility involved. You might want to offer her some money now to help them out on condition that this is seperate from any agreement for child mainatance going forward (i.e. you wont be paying that much in future). This might take the pressure off the mother wanting or needing an agreement for child maintanance as soon as possible, and would help you form a positive relationship.
Now in terms of contact, this can take any form that works for all of you, most importantly your new step daughter. Your suggestion of a contact centre threw me- you would have to pay to use a contact centre if its through choice, they are usually used to keep the child safe because the parent they are meeting poses a risk. If you only want an occasional relationship meeting close to where your step daughter lives you can go to soft play, cafes, cinema, shopping, whatever you find as your shared interests. This is fine, but in my opinion would be quite a 'slack dad' approach - (after a relationship has built up) why shouldn't she be welcome in your home as part of your family? Unless there are factors you havent mentioned in your posts there is no reason why you wouldnt be able to have your stepdaughter to stay reguarly as part of your family once the relationship is there- the amount of involvement depends on how the relationship develops not on what has happened in the past. This includes being involved in important decisions in her life, recieving school reports etc if thats how the relationship develops.
If as you say you do want your step daughter to be part of your family, it would be better to make this clear now, as her mother and partner also need to get their heads round the changes this will mean in their life. Parents work out contact in all sorts of different ways, usually the child travels to spend time at the home of the other parent if the visit is for more than a few hours. Taking into account the distance involved you are mainly going to be thinking about how she can stay with you during the holidays, and possibly weekends during term time if you all feel the travelling is not too much/ to attend your family special occasions.
In terms of starting to establish a relationship you need to think about how your step daughter will be feeling at the moment. Depending on what she has been told, she is likely to feel rejected already as she has never met or heard from her father- she will not understand the adult world. So you need to ensure nothing happens that will cause her to feel rejected again, particuarly while you are getting to know each other. Her mum knows her best, so listen to her opinions on how to approach this. In general, you could read on the internet about introductions for children being adopted for ideas on how to establish a relationship. Something along the lines of sending a photo, letter or video clip introducing yourself and saying how excited you are to meet her. Then you and your husband travelling up to meet her with her mum and step dad for a short visit, maybe repeat this and then get them all to travel down to meet your children and see your house. Then maybe your husband going up to take her out for a few hours on his own or with you, working up to a time when your stepdaughter feels comfortable coming to stay overnight at your house. Presumably your husband's family will be keen to meet her too, so you will need to plan these introductions too.
I have written loads, and this is a lot to take on board at this time I realise. However the approach you take now will set the tone for the rest of your relationship with your step daughter, not least in the way that she feels about your husband and what she percieves to be his feelings towards her. Good luck, I hope it all works out well for all of you.