Keep your tyres for now, you may just have had bad luck.
Punctures are part of life (not that I get many) - just learn to fix one. I'd recommend talcing (talcum powder in the bathroom cupboard) the inside of the tyre or the tubes - it stops them sticking and it's easier to fit. You then just need some plastic tyres levers and your thumbs.
The tyre liners also dead the feel of the tyre. I was getting a puncture at least twice a week a couple of years ago on my commute on the canal after the council trimmed the hedges (thorns). Tried the liners, and whilst they worked, after a few months I was getting random slow punctures. The holes were that small they were difficult to find, even in a bucket of water. I then found one on the edge of where the tyre liner was and it had worn the tube. I removed them and bought better tyres.
Unless you are puncturing regular, keep the tyres for now. My commute is notorious for glass, and only tyres with a good protection band stand up - they get cut to ribbons, but 99% of the glass doesn't get through - I did, however, get a large shard through a couple of weeks ago. It also was raining, so I just ended up with filthy hands from the roadside change of tubes. I fixed the tube later, in the warmth.