My brother is watching SG-1 and a friend is about to start it, so they asked me to write this; I had already done this work for May years ago, so I said ok, sure. In case you want to watch it and are daunted by the size of the series (and there are some pretty poor episodes in the first few seasons), here's my opinion. Your mileage may vary. (Comments are welcome.)
For a full episode guide with photos and synopses, refer to the Stargate Wiki.
101 and 102 - Children of the Gods (part 1 and 2): well, those are the pilot. Absolutely essential, and fun too.
103 - The Enemy Within: pretty good, and establishes setting. Also sees the final organisation of the SGC.
104 - Emancipation: ok but not great episode, absolutely useless to the setting. If you're a feminist, then do watch it.
105 - The Broca Divide: one of my least favourite episodes ever, I really, seriously hate it, but my brother actually enjoyed it.
106 - The First Commandment: irrelevant to the setting, but starts some ethical discussions that will be used quite a lot in the series. Not bad.
107 - Cold Lazarus: avoid. Unless you're a huge O'Neill fan; this episode is pretty bad but it explores his past and personality a bit more.
108 - The Nox: essential and good, 'nuff said.
109 - Brief Candle: beautiful episode, as in chick-flick-beautiful; irrelevant to the story, but I recommend waching it anyway.
110 - Thor's Hammer: good fun and very important to the story.
111 - The Torment of Tantalus: I like it; other people think it's one of the best in the series (I don't agree, but it's great). It's also pretty important.
112 - Bloodlines: so-so, but pretty important to the setting.
113 - Fire and Water: no. Just no.
114 - Hathor: strong taste of the 80s in the writing, but not a bad way to spend an hour, and reasonably important to the story.
115 - Singularity: pretty good writing and minor relevance to the setting.
116 - Cor-ai: I found it a bit boring, but if you're a fan of trial movies, I suppose you'd like it. Not important to the story.
117 - Enigma: ok episode, pretty relevant to the story.
118 - Solitudes: another fun, chick-flick ep, with some small but important relevance to the setting.
119 - Tin Man: one of the first funny episodes, worth watching; also has some very minor importance to the story. (Ok, not really it doesn't; just that a much better episode later is more or less a sequel.)
120 - There But for the Grace of God: great episode, can't be missed.
121 - Politics (part 1 of a 3-parter): first recap story (they became common on season endings), absolutely watch it; it's not only important, but it also recaps the whole season, including the eps you skipped.
122 - Within the Serpent's Grasp (part 2 of a 3-parter): great fun, super important, season finale, seriously, go watch it already.
201 - The Serpent's Lair (part 3 of a 3-parter): does it even matter if it's good? It continues from Politics and Within the Serpent's Grasp, and you watched the other two, so obviously you're watching this one.
202 - In the Line of Duty: so-so but really important.
203 - Prisoners: not really good IMO. There's a better episode later that references this one but you can understand it with the recap only.
204 - The Gamekeeper: keep away.
205 - Need: you don't need to watch this.
206 - Thor's Chariot: good episode, and important.
207 - Message in a Bottle: useless.
208 - Family: ok episode, somewhat important.
209 - Secrets: ok episode, pretty important.
210 - Bane: this episode should be arrested for the crime of sucking.
211 and 212 - The Tok'ra (part 1 and 2): good fun, essential to the story.
213 - Spirits: ignore it.
214 - Touchstone: ok, and relevant.
215 - A Matter of Time: pretty good episode, not very relevant though.
216 - The Fifth Race: very good episode, super important.
217 - Serpent's Song: interesting and relevant.
218 - Holiday: yawn.
219 - One False Step: weird, irrelevant episode, I suppose some people like it but really, wtf.
220 - Show and Tell: not really good, I don't know.
221 - 1969: awesome. You owe this one to yourself.
222 - Out of Mind (part 1 of a 2-parter): not great but necessary.
301 - Into the Fire (part 2 of a 2-parter): not great but necessary.
302 - Seth: unnecessary, but not TOO bad.
303 - Fair Game: super important.
304 - Legacy: ignorable.
305 - Learning Curve: pretty good writing, provoking story. But yeah, utterly irrelevant to the chronology.
306 - Point of View: yes please.
307 - Deadman Switch: passable, not great.
308 - Demons: I hated it. You will too, unless you're a fan of inquisition-style stories. Then it's ok.
309 - Rules of Engagement: interesting writing, somewhat relevant.
310 - Forever in a Day: key episode, not too great though.
311 - Past and Present: great fun.
312 - Jolinar's Memories (part 1 of a 2-parter): yes please.
213 - The Devil You Know (part 2 of a 3-parter): essential.
314 - Foothold: utterly irrelevant but interesting to watch.
315 - Pretense: pretty important and not bad.
316 - Urgo: meh.
317 - A Hundred Days: so-so. Some people find it “the best O'Neill episode” (not me). No relevance.
318 - Shades of Grey: fun and really important.
319 - New Ground: not too bad.
320 - Maternal Instinct: really important, but not really good.
321 - Crystal Skull: about as bad as the one with Indiana Jones in it. Run.
322 - Nemesis (part 1 of a 2-parter): key episode (good too).
401 - Small Victories (part 2 of a 2-parter): key episode (good too).
402 - The Other Side: provoking story.
403 - Upgrades: ok fun, and “relevant” to the emotional side of the story.
404 - Crossroads: pretty important one.
405 - Divide and Conquer: good and important.
406 - Window of Opportunity: I love this episode, seriously. I also love froot loops.
407 - Watergate: interesting, tense episode in a different tone.
408 - The First Ones: ok fun, of minor relevance.
409 - Scorched Earth: unnecessary, but not too bad.
410 - Beneath the Surface: interesting. You may like it or hate it, but try. No relevance to the story.
411 - Point of No Return: intensely fun to watch, of minor relevance.
412 - Tangent: great tense episode.
413 - The Curse: great episode. Can't say any more w/o spoilers.
414 - The Serpent's Venom: absolutely necessary.
415 - Chain Reaction: necessary.
416 - 2010: fantastic.
417 - Absolute Power: key episode.
418 - The Light: you can live without this one, but not too bad.
419 - Prodigy: ok fun.
420 - Entity: best avoided.
421 - Double Jeopardy: important and fun.
422 - Exodus (part 1 of a 3-parter): essential.
Here you want to just watch everything; the series found its pace and no episodes are worth skipping.
Now it depends. If you became a huge fan of the series, go on watching. Otherwise, pretend the series ended with Moebius; these last 2 seasons are hugely less interesting than the first 8. Just treat yourself to episode 1006, title “200”. Then watch the second movie, “Continuum” (you can ignore “Ark of Truth” as it's the end of the 9th/10th seasons storyline).
The first episode of Atlantis is simultaneous with SG-1's 803 “Lockdown” and has a bit of cross-over with that and the preceding two. So the right order is 801 and 802, then Atlantis 101 and 102, then 803. You can watch season 8 and Atlantis season 1 any way you like (as Atlantis is isolated by that time). Then Atlantis season 2 interacts a lot with SG-1 season 9, and same for A3 and SG-1 10. So if you're watching 9 and 10, the best thing to do is to watch one episode of SG-1, then one of Atlantis, alternating, the way they were originally released.