The Blog will help you a lot. From Experience, in order to get married here, check to see what documents you need to bring from the U.K. Make sure those documents are notarized and have an apostille. Second bring two copies of all documents. When you get here you will need to get a non-inpedment notarized at your embassy here in Ukraine. Then you need to take all documents to the foreign ministry to be approved.
Then with all of the documents and approvals in hand you can get a civil marriage. Once you register it takes about 30 days. Once you are married you will need to get a Visa D, which is a temporary 45 days visa. Being from the U.K. it is easier to return to the U.K. to get it. For Americans I recommend going to Moldova with all of the correct documents. With that Visa you can return to Ukraine and get your first one year extension. Prior to one year you will need to apply for a second one year visa. After two years you are eligible to receive a permanent residence in Ukraine. But prior to obtaining the permanent visa you will need to get a third one year extension. After three months you will be able to apply for the permanent residence. A friend of mine just went through this process.
Good luck with OVIR. I do not know how it is in Kiev, but they are a $$$$$$ business to get your documents done.
Good luck, I hope this helps you. Check the blog that Grey advised you. I have been in Kharkiv for many years and I have enjoyed living in Ukraine. On the medical insurance, you will need it for your visas. I have never used it. The doctors and hospitals will not take it. Only cash. Welcome to a new world. Not that expensive. I do not know your financial status, but things are more affordable here in some ways. But not in others.
I will tell you if you are able to find the Right Ukrainian Flower, they are wonderful and loving wives. Make her feel important in your life and give her lots of love. She will grow with you and love you beyond all measure. I have never regretted my decision to marry my wife and live in Ukraine. I miss the States at times, but home is where your family lives.
This part I will really stress. Make sure all of your documents are correct and with all of the proper notarization and Apostille. In Ukraine they are very demanding when it comes to documentation. Make sure they are correct and bring two copies.
All the very best.