Sorry if I was not clear enough, actually (in my case) order search would be slightly more important, because order search is really slower than product search (I have 40,000 orders in my db), but of course an Algolia product search would be great as well.
As far as product search is concerned, yes
are enough. The ability to add some metafields to the search would also help a lot (for example, I sell travel maps, they have ISBNs that is recorded in an ISBN fields, and does not match necessarily the SKU - I tend to rely a lot on this metafield to find products).
For display, in addition to title, sku and price, I need at least to see the stock level, cost of goods, and product categories. This view should be as customizable as possible, since I am pretty sure each merchant has its own personal but crucial habits.
(Woocommerce 2.6.9 / Wordpress 4.7 / Woocommerce plugin 0.5.1 / Algolia Search 1.6.0)