It's not really too complicated. You can basically stick to the release order (of the original books, the English translations seem to lag behind quite a bit and might be out of order), as depicted by Wikipedia, except for a minor switch. Well, first of all, there are basically three different kinds of stories concerning the Witcher written by Sapkowski.
(The spoiler blocks in the answer are not really spoilers at all but only very rough details that could as well be blurbs from the backs of the book, but I blocked them nevertheless as you can never be sure what people really consider a spoiler.)
The short stories
There are the more-or-less independent short stories, primarily published in Sword of Destiny (Miecz przeznaczenia, 1992) and The Last Wish (Ostatnie zyczenie, 1993).
The individual short stories are largely independent of each other and could maybe even be read completely discontinuous across book boundaries. However, there are a few connections between some of them. In addition to that, The Last Wish actually features a frame story to serve for the short stories to be told as flashbacks (the frame story itself is not too relevant for the bigger picture, though, as much as I remember). So it is indeed advised to read the books as a whole each.
Now what about the order of the two books? In fact you should read The Last Wish before Sword of Destiny. While they aren't too connected, the in-universe chronological order is rather this way (as Sword of Destiny actually ends with
the war against Nilfgaard beginning, which is the major war that the novel series is set against
and because both books feature short stories that are highly relevant to the novel series, in addition to other minor character developments.
This slight order switch is grounded in the fact that many of the stories from The Last Wish were actually published in an earlier book (The Witcher (Wiedzmin, 1990)) and only collected into the frame story in The Last Wish later.
(The collection Something ends, Something begins (Coś się kończy, coś się zaczyna, 2000) contains two stories related to Geralt but as much as I know (haven't read them admittedly) they don't really have much significance for the broader matters at all (one of them is supposedly depicting the marriage of Geralt and Yennefer as the collection itself was supposedly written for a friend of Sapkowski who was getting married or something like that). Neither does there seem to have been any effort in translating Something ends, Something begins into the English language yet.)
The novel series
Then there's the 5-part series of novels, comprised of Blood of Elves (Krew elfów, 1994), Time of Contempt (Czas pogardy, 1995), Baptism of Fire (Chrzest ognia, 1996), The Swallow's Tower (Wieza Jaskólki, 1997), and Lady of the Lake (Pani Jeziora, 1999). Those indeed tell a closed and continuous story and should thus be read one after the other in release order.
This series is chronologically set after the short stories and should thus be read after them (as also released afterwards). It does not depend too closely on all the short stories, but there are a few important connection points:
- There's the whole story about Cirilla, Geralt's "child of surprise", about whom the series is primarily centered.
Her background was first introduced in the short story "A Matter of Price" from The Last Wish and later continued in "The Sword of Destiny" and "Something More" from Sword of Destiny. (Ignoring possible additional minor references to Ciri in other short stories.)
- There are other minor characters recurring in some of the short stories and referenced throughout the novel series, foremost Geralt's on-and-off love interest Yennefer of Vengerberg,
a relationship primarily developed in "The Last Wish" from The Last Wish and picked up later in "The Bounds of Reason", "A Shard of Ice", and "Something More" from Sword of Destiny.
And then there is the rather new Season of Storms (Sezon burz, 2013). This is a standalone novel supposedly set during the time of The Last Wish or between that and Sword of Destiny.
In particular the striga haunting Temeria is mentioned at the end of Season of Storms. So it seems to be set before the first story "The Witcher" from The Last Wish, which in turn leads to the frame narration that engulfs the rest of the flashback short stories in that book.
While it doesn't rely on any of the short stories per se, it employs major characters introduced in them, especially Dandelion and to a smaller degree Yennefer, and afterall Geralt himself and his whole background as a witcher, and doesn't care much to reintroduce them again. So it definitely helps to have read The Last Wish at least.
Since it is pretty much a prequel to the novel series, it naturally doesn't really spoil anything from there. However, it uses a minor character from the novel series, but only in two short interludes and you don't really have to know who she is (or will become) to fully grasp the story there, it's mainly just a small recognizing "aha" moment (that might as well work the other way around). And while it is interesting to see the slightly ambiguous ending of Season of Storms in relation to the ending of the novel series regarding its motifs, that connection might as well work the other way around, too. You certainly don't have to know the ending of the novel series at all and neither is it really spoiled.
It should thus not be too relevant if you read it after The Last Wish, between the short stories and the series, or just after all the other books. But sticking to release order (i.e. reading it last) can't hurt, since it was certainly published this way and likely intended by Sapkowski to also be consumed that way, especially seeing the large 14-year gap since the release of the novel series.
So long story short, you should be set fine when just sticking to (original) release order but switching the two short story collections, pretty much like you already outlined it in your question:
- The Last Wish
- Sword of Destiny
- Blood of Elves
- Time of Contempt
- Baptism of Fire
- The Swallow's Tower
- Lady of the Lake
- Season of Storms (might also be consumed earlier)
The video games are not particularly canonical for the larger matter and are only an unofficial continuation of the books (as also discussed in this related question and its answers) and I doubt Sapkowski was actually involved in creating them at all (personally they are quite enjoyable, though, and actually what brought me to this universe, too). However, they are set after the novel series but only loosely reference past events and don't really spoil anything there, nor require anything to be known beforehand. They do to some degree replicate some of the things from the books in the video game as actual plot points, though, be that only as faint allusions. But you can really play them whenever you want.
The Polish television series from 2002 is actually an adaptation of the short stories from The Last Wish and Sword of Destiny. It was also released before the TV release in 2001 as a movie in a more compressed form. While the TV-show/movie were largely panned by critics, fans, and the author himself, it is at least an interesting watch if you have read the two short story collections and want to see them in audiovisual form.