OK - it depends where your interests lie - for Thomas Burns and his environment your next best bet would be to access as many of the maps and Directories on-line from 1900 onwards to see the changes in work and living patterns around the addresses you know about. If you want to know more about the development of Toxteth itself, there are two books in which you may be interested - The Illustrated History of Liverpool's Suburbs (Illustrated History) by David Lewis which covers most of the Liverpool outskirts as well as Toxteth, some of which you may find that your relatives lived and worked in and The History of the Royal and Ancient Park of Toxteth by Robert Griffiths - but I wouldn't bother with either unless you are really interested in the history of Toxteth (I have just checked on Amazon UK and they are both in stock at reduced prices - a lot less than I paid a few years ago when they were published!). You might also make progress through sailor and shipping records at the National Archives in London, although you would normally need to visit and research through paper files - they are gradually digitising their document index and even more gradually making sets of documents available on-line for a download fee of the scanned images - you never know what you might find - try a name search on their website (www.nationalarchives.gov.uk). Thomas may also have served in the merchant navy, Royal Navy or army during WW1 and increasing numbers of official war records are now appearing on-line. Otherwise you will have to wait until 2011 for publication of the 1910 census!
If you find further info, you may find a Genealogy.com or an Ancestry.co.uk discussion forum related to the topic through which you may make contact with someone who can help you further (e.g. http://genforum.genealogy.com/englandcountry/liverpool/ or http://boards.ancestry.co.uk/localities.britisles.england.lan.lswlfhs/mb.ashx