I've used duvets for years and found that you need to check out different lines because the duvets can vary so much from year to year. That said, I do think that LL Bean has some dependable options as does Bed, Bath, and Beyond; Pottery Barn; and some department stores.
If you are looking for a synthetic fill, try looking for one that seems to have a bit of firmness in the padding. That usually means a thicker batting which equals more warmth. And don't be afraid to launder a duvet if it seems to be getting thin in spots. Depending on the size of your washing machine, you can do this at home or, if it's a king-size duvet, in a commercial machine. You can do this with both down or synthetic duvets but make sure to use just a small amount of low-sudsing detergent in the wash cycle and follow with an extra rinse cycle to make sure all the soap gets removed. Use a dryer (either home or commercial) on medium heat to dry the duvet and throw in a clean tennis ball (or 2) while drying to keep the batting or down from clumping. I usually finish by air-drying for a day or two before putting the duvet back on the bed. Washing can completely restore a duvet to its original condition.
My sister opted for using 2 single-sized duvets on her king-sized bed to make it easier for her to wash the duvets in her home machine. Works very well.
The key to keeping a duvet in place is to make sure the cover is the same size, or even a bit smaller, than the duvet so the duvet doesn't slide around inside. Some covers (and duvets) come with snaps or ties that you can use to keep the duvet in place, but I've never found that I needed them.
Duvet covers can be found almost everywhere these days, but I look for a silky smooth, washable cotton because we don't sleep with a top sheet--just the duvet. My duvet covers get washed every week when I change our bedding. I like white duvet covers and second Angie's recommendations. I've also found Pottery Barn and LL Bean a good source for covers. These two companies offer a range of fabrics (including flannel covers which are cosy in the winter) and patterns if that is more towards your taste.