word choice - Have you tried XYZ before?

I English I can ask somebody if they've experienced or sampled a food or drink, or even an activity with this verb:

• Here try this and tell me if you like it.


• I tried koregusu once but I didn't like it.



• You don't have to eat it but at least try it.


• I like spicy food so I really want to try taka-no-tsume.


• You can't say you don't like tequila if you never even tried a good one!

Non-food/drink examples:

• Did you ever try scuba diving?


• I tried hitchhiking once but I prefer to travel by bicycle.

I'm having trouble finding a word, phrase, or pattern, to express this sense of try.(I know it overlaps with the other senses of try in English.)

These are the closest Japanese terms I could find. Do they do the job?

• 味わう


• 嘗める


• 試す


• 味見する