Visa with a single ticket?

Not sure exactly which forum to place this in, since it covers both to a degree…

I’ll be flying out to Taiwan mid-August from the UK. I was hoping it would be possible to get just a single ticket, since it would give me that much more money to spend while I’m there (looking at £800 return with Cathay, whereas there’s an EVA Air single for £470). So do all the visa’s require a return ticket?

Alternatively, if I sorted a job before I arrived in Taiwan, would it then be possible to purchase a single and get a visa?

Any other advice on the best airline to go for would be most appreciated. I went out to Taiwan for a month last year, flew with KLM, which wasn’t bad, but I think there is better for the same price.