Hi Kenny
You do not need a service number to research men in this period, nor even a regiment, as the surviving papers for men discharged 1883 to 1899 are in alphabetical order. These are in WO97. The indexes for these are in the blue folders near the Army Lists
The Muster and Pay Lists are in WO12 up to about 1885, and WO16 afterwards. These peter out in the mid 1890s. The indexes for these are in the red folders behind the main enquiry desk. For the musters you need to appreciate that most regiments had two battalions and a Depot, and each had separate musters. The Depot ones are normally in the back of the ‘home’ battalion. Musters as late as these hold a lot of information, and you need to go through all the sections, especially if you find he was being discharged or transferred as additional information could be in other sections.
The musters for when he was recruited or discharged should give useful FH information such as when and where born, occupation etc. WO12, 16 & 97 are original documents so you will need a reader’s ticket, which you should order in advance to save time.
http://www.nationalarchives.gov.uk/militaryhistory/army/step4.htm Original documents take 45-60 minutes to arrive. While you are waiting you can look through the Army Lists, both official and Harts (which are better), and search the medal rolls – on microfilm in WO100 (blue index) – if you find that his regiment were involved in any campaigns while he served..
Once documents have arrived you can order more, without waiting to return the first ones ordered.
Ken
