By a "keep", I assume you mean a castle in general, rather than the specific building within a wider castle. This can be quite a tricky question to answer, since "castle" can encompass a huge range of fortifications from massive semi-urban precincts to tiny, rural outposts. A lot hinges on the actual function of the castle in question: is it a primary manorial residence? A lesser property of a major lord? A royal vil? An urban garrison?

I'm going to make a further assumption that your party haven't somehow taken possession of a major urban or manorial fortification like Bristol or Wallingford but have instead been given a relatively minor rural castle, possibly with attendant village. As a prime example, I'll look at Peveril Castle, which is a small royal castle built to extend contol across the Peak District in the Twelfth Century. Unless it's functioning as a primary residence or there's the risk of invasion, castles really don't call for much by way of manpower. Apart from being reinforced during the war of 1173/4, the standing garrison at Peveril castle consisted of a porter and two watchmen. In the absence of the king (or in the case of the lord in any other castle), the castle was managed by a castellan. There would have been few other staff on site beyond the castellan's own servants and kitchen staff, as any lord would have brought their own staff with them when travelling. There would perhaps have been falconers or huntsmen, and likely a bureaucratic staff to assist with local administration.

Castles by themselves don't tend to be economically productive sites. Although larger castles would have had workshops within them, these would have been primarily for the use of the castle and its personnel. Castles did function as administrative centres, and secure sites for the collection and storage of taxes and the lord's personal money, but within the extra-mural community, valuables are more likely to have been secured within the parish chest. A castle's prime economic function was essentially to exist. The presence of a castle and the protection and stability it inferred most commonly led to the accretion of extra-mural settlement and agriculture, and it was this that was economically important.