Piecemeal is not a dirty word. Buying a set often means ending up with some sizes that don't get used much and just collect dust. Usually the smaller pieces. Unless it's really important to you to have an aesthetically identical set, it's probably better to buy the pieces (sizes) you use most & pay for quality construction. It's still possible to find deals if you look around. Quality tools, cookware or otherwise are a pleasure to use & will last a long time with modest care. Well made stainless can last a lifetime, with the likely exception of the handles. A heavy metal handle might outlive you, but the more common resin/bakelite/plastic ones often start to crack and break after 10-15-20 years. Other than the handles, I have stainless pieces that are >20 years old & still going strong.
Still that doesn't mean that stainless is necessarily the best choice for all of your pieces. Does your wife have strong preferences? What does she like to cook with, treasure & hate? Tastes do vary. For myself I hate Pyrex (glass) pots & bakeware, aluminum & stamped steel. I'm not overly fond of teflon either, but grudgingly admit it's useful for a few special purpose dishes. The majority of my cookware is stainless & for general purpose use, it is durable & has few drawbacks. The main one IMO is that stainless doesn't heat evenly, so you will often see it clad with other metals. It's not a big issue with most tasks, but there is some tendency towards hot spots, so you might burn a sauce if you aren't careful. So I prefer copper (expensive, hard to clean) for say, a Bolognese reduction. And cast iron for yet another task. Most will agree that quality construction is desirable & that is about where the consensus on what is best ends.
I'd say that stainless-clad i.e. quality stainless is a good bet for those who want quality pieces but don't obsess over subtle distinctions. However if she already has strong opinions about her cookware or you know her to be fussy, discerning or obsessive in general, then perhaps you solicit her opinions before buying anything. In any event, what materials make for the best cookware is a theme that shows up regularly in forums like egullet, chowhound, cheftalk, etc if you want to read more opinions.