Lee Enfields would've been pretty new. Probably a few Lee-Enfields and then Martini-Henrys or something. I don't know though.
Lee-Enfields had been widely issued by this time. Lee-Metfords were usually restricted to second-line and support troops. Martine-Henry rifles were mostly used by poorly equipped colonial troops. The New Zealanders, for example, were intially armed entirely with Martine-Henry rifles. The Canadians, on the other hand, were well armed with Lee-Enfields and a number of American made sidearms, mainly Colts.
Another weapon the Boers used a number of was the Krag-Jørgensen, a heavy and not particularly useful Norwegian bolt-action.
As Van_Hulstein states, the Boers had the advantage in regards to arms. The Lee-Metford had serious issues, not the least of which was the use of black-powder. The Lee-Enfield solved some problems, but was still plagued by others, like bad sights. By World War 1 the Lee-Enfield was superior to the Mauser in almost every regard, but during the Boer War they couldn't even take chargers.
If you give the Boers Lee-Metfords, you should think of a way to represent the Lee-Enfield ammunition destroying the rifle. It was the same bullet and cartridge, but the Lee-Metford could only handle black-powder, whereas the Enfield used cordite propellent.