Let's see if I can map out Star Trek as a franchise. Keep in mind, I'm a hardcore Trekkie compared to my real life friends, but probably a casual fan compared to my fellow TrekBBS Trekkies.
I'm going to drop a reasonable viewing order for a "new" fan, then try to morph than into a proper timeline.
Star Trek (original) + Star Trek (animated) + 6 movies
The Next Generation (decades after TOS movies) + 4 movies
Deep Space Nine (began during TNG S6, overlaps with GEN, FC, INS)
Voyager (began during DS9 S3, overlaps with FC & INS)
Enterprise (franchise prequel - 110 years before TOS)
Reboot trilogy (Star Trek / Into Darkness / Beyond)
Discovery (began as 10 years before TOS)
Short Treks (companion to Disco)
Picard (20 years after Nemesis)
Lower Decks (following Nemesis - 4th series to TNG-DS9-VOY)
Prodigy (5 years after VOY ended)
Strange New Worlds (following Disco S2, TOS prequel)
That's an easy way to explain Star Trek to a newbie, yes? Now let's make this a timeline.
Because Time Travel
1986: The Voyage Home (when they're in the past)
2024: Picard S2 (mid-E3 through most of E10)
2063: First Contact (when they're in the past)
Prequels
2151-55: Enterprise (4 seasons)
2161: Enterprise finale
2256-58: Discovery (S1-2)
2259: Strange New World (S1-2)
Reboot Trilogy
2258: Star Trek (2009)
2259: Into Darkness
2263: Beyond
The Originals
2266-69: Star Trek (3 seasons)
2270: Star Trek (animated)
2273: The Motion Picture
2285: The Wrath of Khan / The Search for Spock
2286: The Voyage Home
2287: The Final Frontier
2293: The Undiscovered Country / Generations (flashback part)
Brace yourselves!
2364: The Next Generation (S1)
2365: The Next Generation (S2)
2366: The Next Generation (S3)
2367: The Next Generation (S4)
2368: The Next Generation (S5)
2369: The Next Generation (S6) / Deep Space Nine (S1)
2370: The Next Generation (S7) / Deep Space Nine (S2) / Enterprise finale
2371: Deep Space Nine (S3) / Generations (TOS / TNG film) / Voyager (S1)
2372: Deep Space Nine (S4) / Voyager (S2)
2373: Deep Space Nine (S5) / Voyager (S3) / First Contact (2nd TNG film)
2374: Deep Space Nine (S6) / Voyager (S4)
2375: Deep Space Nine (S7) / Voyager (S5) / Insurrection (3rd TNG film)
2376: Voyager (S6)
2377: Voyager (S7)
2379: Nemesis (4th TNG film)
2380: Lower Decks (S1)
2381: Lower Decks (S2)
2382: Lower Decks (S3)
2383: Lower Decks (S4) / Prodigy (S1)
2384: Lower Decks (S5) / Prodigy (S2)
2285: Children of Mars (Short Treks)
2399: Picard (S1)
2401: Picard (S2-3)
2402: Picard (finale ending)
The Distant Future
3188: Discovery (S3 premiere)
3189-91: Discovery (S3-5)
3221: Discovery (finale flashforward)
43rd Century - Calypso (Short Treks)
Did I get this right? Nitpicking, commence!

Star Trek (original) + Star Trek (animated) + 6 movies
The Next Generation (decades after TOS movies) + 4 movies
Deep Space Nine (began during TNG S6, overlaps with GEN, FC, INS)
Voyager (began during DS9 S3, overlaps with FC & INS)
Enterprise (franchise prequel - 110 years before TOS)
Reboot trilogy (Star Trek / Into Darkness / Beyond)
Discovery (began as 10 years before TOS)
Short Treks (companion to Disco)
Picard (20 years after Nemesis)
Lower Decks (following Nemesis - 4th series to TNG-DS9-VOY)
Prodigy (5 years after VOY ended)
Strange New Worlds (following Disco S2, TOS prequel)
That's an easy way to explain Star Trek to a newbie, yes? Now let's make this a timeline.
Because Time Travel
1986: The Voyage Home (when they're in the past)
2024: Picard S2 (mid-E3 through most of E10)
2063: First Contact (when they're in the past)
Prequels
2151-55: Enterprise (4 seasons)
2161: Enterprise finale
2256-58: Discovery (S1-2)
2259: Strange New World (S1-2)
Reboot Trilogy
2258: Star Trek (2009)
2259: Into Darkness
2263: Beyond
The Originals
2266-69: Star Trek (3 seasons)
2270: Star Trek (animated)
2273: The Motion Picture
2285: The Wrath of Khan / The Search for Spock
2286: The Voyage Home
2287: The Final Frontier
2293: The Undiscovered Country / Generations (flashback part)
Brace yourselves!

2364: The Next Generation (S1)
2365: The Next Generation (S2)
2366: The Next Generation (S3)
2367: The Next Generation (S4)
2368: The Next Generation (S5)
2369: The Next Generation (S6) / Deep Space Nine (S1)
2370: The Next Generation (S7) / Deep Space Nine (S2) / Enterprise finale

2371: Deep Space Nine (S3) / Generations (TOS / TNG film) / Voyager (S1)
2372: Deep Space Nine (S4) / Voyager (S2)
2373: Deep Space Nine (S5) / Voyager (S3) / First Contact (2nd TNG film)
2374: Deep Space Nine (S6) / Voyager (S4)
2375: Deep Space Nine (S7) / Voyager (S5) / Insurrection (3rd TNG film)
2376: Voyager (S6)
2377: Voyager (S7)
2379: Nemesis (4th TNG film)
2380: Lower Decks (S1)
2381: Lower Decks (S2)
2382: Lower Decks (S3)
2383: Lower Decks (S4) / Prodigy (S1)
2384: Lower Decks (S5) / Prodigy (S2)
2285: Children of Mars (Short Treks)
2399: Picard (S1)
2401: Picard (S2-3)
2402: Picard (finale ending)
The Distant Future
3188: Discovery (S3 premiere)
3189-91: Discovery (S3-5)
3221: Discovery (finale flashforward)
43rd Century - Calypso (Short Treks)
Did I get this right? Nitpicking, commence!

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