It wouldn't have been mineral wealth in 1806, not in any meaningful way. The Cape Colony produced wool and provisions for ships, but that's about it. Mineral strikes really come much later, with some hints in the 1850s/60s but really taking off with New Rush (Kimberley) in the 1870s.

The strategic argument is really the soundest one. The British handed Batavia (Djakarta) back to the Dutch after the Napoleonic Wars, but the Cape of Good Hope was payment for the debts of the Dutch state to Britain. Although Amiens had handed it to the Batavian Republic--a Napoleonic creation--the question was whether it would go to the Dutch government. The VOC (Dutch East India Co.) dissolved at the end of 1799, so they did not exist to make a claim on it. For Britain, this was security for lines of communication to India and increasingly China, and it was very clear in the wake of 1815 that Britain's mercantile and naval power would be global so the facilities in Table Bay and, soon enough, in Simon's Town would be essential to that position. Napoleon had proven that a hostile power might cut off the overland communications route, which would remain a threat until the 1880s, and until the canal the traffic was mostly that--information, and perhaps a few diplomats or other individuals. Even with effective control of the canal at Suez after 1882, British strategic thinking did not shift from the Cape route until 1890.

After the retention of British power in the Cape was secured by agreement with the Dutch crown, however, and two wars against Xhosa-speaking polities in the east had proven how difficult and fractious the trekboers were, government began to promote the prospects of the Zuurveld and areas inland from Port Elizabeth as havens for land-hungry British settlers. The famous 1820 settlers were one of many groups who went looking for free land and occupied territory on a semi-military tenure, which had the added benefit to the colonial government of hopefully Anglicizing the Eastern Province of the colony. Of course, a lot of the policies and ethics they also brought clashed with some of the local trekboers, but that's another story.

I'd point you at a variety of places in Elphick and Giliomee, eds., The Shaping of South African Society 1652-1840 (1989) on this. It hasn't been superseded, although volume 1 of the Cambridge History of South Africa updates a variety of things. Initially it really is strategic consideration along with the settlement of debt.