Overlap liners are my personal favorite. When properly installed they fit better than any other type of liner, like the beaded or J hooks. The liner can be stretched over the existing framework allowing the water to lay the bottom in smooth. The walls can be pulled tight and all the excess liner tucked back under leaving smooth walls and an even overhang on the outside. What more could you ask of a vinyl liner.
Prints and patterns are all the rage with vinyl liners these days. Yes they are very nice and colorful when new. Liners tend to fade quickly from the exposure to the sun and pool chemicals. How long will that expensive pattern stay looking nice? Not long enough I am afraid. I prefer an inexpensive blue liner myself. That's just my personal opinion.
When installing a liner in this way be sure the corners on all of the caps are smooth or well covered with duct tape. Doughboy pools are designed for this type of installation but many other brands are not. Sharp corners can easily tear the liner. Use plenty of tape and any brand of pool can have a vinyl liner stretched into it in this fashion.
The biggest problem people have with vinyl liners of all types is leaks. Finding and patching holes in liners is sometimes fast and easy, sometimes a real pain. Click this link to learn more about finding holes in vinyl liners.
Another real problem with vinyl is dry rot. In some cases it cannot be prevented, but with proper care the damage can be minimized. Most dry rot will occur above the water level on the side of the pool that gets the most afternoon sun. Providing some shade for this area of the pool is one way to control dry rot. Keeping the water level as high as possible is another.
Find a full selection of vinyl liners at Amazon.