Shopping online can be a great option for those of us with lower budgets, but looking for higher quality items. Amazon has a lot of crappy stuff on it, but they also have nicer stuff if you know what you're looking for, and are willing to invest the time to read gazillions of reviews, and do your research.
Also, you can stalk designer items you'd like to snag online and wait for them to go on sale. Or in some cases, buy them lightly used, for example on ebay.
Lands End has quality stuff that is not terribly pricey, and you can get pretty good discounts with them by using special offers or by shopping sale and clearance items toward the end of a season. They still make sturdier tees and nice sweaters, read the reviews to find out which ones. But beware of nutty vanity sizing with them. Read their size charts, and then keep in mind that even if you go by the size charts, their clothing is not cut to be as close fitting as some of us younger women may be used to, so shop accordingly.
100% cotton sweaters, I think are fairly easy to care for, and are pill resistant.
Personally I have had bad experiences with a lot of acrylic sweaters I've owned because they look great in the shop and then go downhill so fast with washing and wearing. A lot of them just look nasty and all matted-and-furry or pilled-like-crazy so soon, that cheap as may have been, it was not worth the investment.
Silk sweaters can be really nice looking for a lighter sweater. And can be bought at fairly reasonable prices sometimes, especially in blends with cotton like here
And if you can afford to invest in some lower-end cashmere, some of it is supposedly made to be pill-resistant. Just beware of scratchiness when trying on or reading reviews.