Harnesses all do the same basic job but with slight variations. Beginner/outdoor centre harnesses tend to be fully adjustable but short on padding. Once you come to buy your own you'll want a bit more cushioning.
You can also buy fixed-size leg loops, although this depends whether it will only be getting indoor use or whether there's some mountaineering on the cards, in which case extendable leg loops are a must to accommodate the extra layers. The number of gear loops - for nuts, cams etc. - also varies depending on intended use.
