Straight up cooking oils. Sunflower and vegetable in particular. Cheap, no particular odour or taste, totally safe, always to hand (important when regular re-oiling will prolong the life of the woodware being regularly scrubbed in the washing up). A possible negative is the particular yellow colour: I personally don't think it goes perfectly on blond woods like sycamore, but I still use it for these, and it is possible to get cooking oils of a lighter hue. When I was carving spoons for sale, an added benefit was that buyers responded well to the idea of maintaining their spoons with cooking oil - it's something they all have and can understand.
If you want to used linseed, do not used commercial 'boiled linseed' - it's not just boiled, it has heavy metal drying agents added. 'Raw' linseed should be fine, but check your sources. Advise against olive oil. The story goes that it can fail to harden in the wood and can go rancid. Something to do with it having a relatively high melting temperature (you may have seen it set in it's bottle in a cold kitchen). I've never experienced this because I've never used olive, but I did meet a lady at a craft show who'd had it happen to a cutting board. I don't know how accurate that all is, but I myself wouldn't choose olive anyway, on account of the colour/flavour/smell. Walnut oil (again a cooking oil) is said to go off (harden) well and relatively quickly - if you like or can live with the flavour (not nice in cereal bowls!). I've used sesame oil to deliberately impart scent and flavour to some spoons as part of an oriental-food-themed gift; that was fun.
