Under $100 is a tall order. I agree with PP that an All-Clad skillet is a wonderful and life-long thing, but it's not in the budget for someone in your sister's situation.
I would not buy T-fal nonstick, or any cheap nonstick. They'll scratch, they won't last, and they may end up shedding Teflon or God-knows-what into your food. Plus, they're thinner metal so are prone to hot spots.
For the general all-purpose skillet, I'd go with cast iron. It's not that hard to learn to care for cast iron--just use non-stick utensils, don't scrub with soap or abrasives, and occasionally re-season with oil, shortening, or bacon fat. With some seasoning, it's as good as nonstick. (I do eggs in mine all the time.) I would to with the 10" Lodge:
http://www.amazon.com/Lodge-Logic-Pre-Seasoned-Skillet-10-25-inch/dp/B00006JSUA/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I3KMLS6VW2AT9D,
plus an 8" Emerilware nonstick for all those quick-saute-for-one jobs:
http://www.amazon.com/Emeril-All-Clad-E9200264-Anodized-Nonstick/dp/B00284B9OM/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I27LU9RSKW210" target="_new" rel="nofollow">
http://www.amazon.com/Emeril-All-Clad-E9200264-Anodized-Nonstick/dp/B00284B9OM/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I27LU9RSKW210.
I have both of these and use them ALL the time.
(If she doesn't want to get into cast iron, you can get a duo of Emerilware nonstick skillets instead for about the same price:
http://www.amazon.com/Emeril-All-Clad-E919S264-Anodized-Resistant/dp/B00284B9QK/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I24KVLLI0BOOBQ)
She'll need saucepans and a big pot (Dutch Oven). There's one school of thought that says sets are a waste because they include stuff you don't need, but the fact is, you've gotta have saucepans, and new, individual pieces are pretty expensive. Entry-level sets can offer real savings.
Though I wouldn't buy T-Fal nonstick or ceramic, T-Fal does have this entry-level stainless set, that's all-purpose and (amazingly) cheaper than Farber and Revere. The price makes this look like a hell of a deal:
http://www.amazon.com/T-fal-C811SA64-Elegance-Stainless-Dishwasher/dp/B000EMDXFI/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I1UR8T960OG0BH
At about $36 for the 2 non-stick skillets and $69 for the T-Fal set, that's just over $100.
For $100 more, she could get a much much nicer stainless set that looks like terrific value and should last a long time:
http://www.amazon.com/Whole-Clad-Tri-Ply-Stainless-Induction-Cookware/dp/B004HBGIBI/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=INSDSMCRTYSY3
The advantage of this set is the aluminum core (the part that conducts heat evenly) is not just on the bottom of the pot, it goes up the sides as well, providing even heating all-around. This looks like All-Clad quality at a fraction of the price.
(According to amazon, the same set is available used from a scratch-and-dent clearance vendor for $89--just $20 more than the entry-level T-Fal set.
http://www.amazon.com/gp/offer-listing/B004HBGIBI/ref=dp_olp_used?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=INSDSMCRTYSY3&condition=used
She's going to need utensils:
http://www.amazon.com/Calphalon-3-Piece-Wood-Utensil-Set/dp/B001DSGQTW/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=IZ0LECH19026S
http://www.amazon.com/Calphalon-FN04-Nylon-Slotted-Turner/dp/B000IVAJ7K/ref=sr_1_18?s=home-garden&ie=UTF8&qid=1371953509&sr=1-18&keywords=turner
http://www.amazon.com/OXO-Good-Grips-Swivel-Peeler/dp/B00004OCIP/ref=sr_1_1?s=home-garden&ie=UTF8&qid=1371955141&sr=1-1&keywords=oxo+good+grips+vegetable+peeler
A cutting board:
http://www.amazon.com/Da-Vinci-Natural-3-Piece-Cutting/dp/B0049M7QQ6/ref=wl_it_dp_o_pC_S_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=IMHNWOBOLYQTU
And the most important and useful kitchen tool ever (after the skillet), IMO:
http://www.amazon.com/Progressive-International-Stainless-Steel-Locking/dp/B000LCOY04/ref=sr_1_3?s=home-garden&ie=UTF8&qid=1371953416&sr=1-3&keywords=tongs
Total cost:
8" & 10" Skillets $36 (with the cast iron, $3 more if both Emeril nonsticks)
Stainless pots set $69
Utensils (incl. tongs): $36
Cutting Boards: $13
Total: $154
With the nicer whole-clad set, $100 more. Or $20 more if she buys that set used (which is what I would do if I were in my 20s with the cooking knowledge of my 40s).
Finally, she'll need some knives. That's a whole separate subject, with a wide range of options, opinions, and prices.
On her rock-bottom budget, I'd go with Chicago Cutlery. She'll need a chef's knife (or can substitute santoku if she prefers, either one is $10) and a paring knife ($6). For an extra $10, a serrated bread knife is also handy. You can get through life with those 3 knives--you don't need a big fancy set and a block.
Chef's knife: [url]http://www.amazon.com/Chicago-Cutlery-Essentials-8-Inch-Knife/dp/B004TFDEPK/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I6KRN103L1O5T
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Santoku:
http://www.amazon.com/Chicago-Cutlery-Essentials-7-Inch-Santoku/dp/B004TFDFAO/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I3678YBXG3WDQ8
Paring knife:
http://www.amazon.com/Chicago-Cutlery-Essentials-2-Inch-Parer/dp/B004TFDFPE/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=38BTP2RQIJ4NM&coliid=I3QFRVPZUWO76J
Bread knife:
http://www.amazon.com/Chicago-Cutlery-Essentials-8-Inch-Bread/dp/B004TFDG7G/ref=wl_mb_hu_m_2_dp
There you go, for $180, a basic starter kitchen outfitted.