I disagree with your list. The Last Outpost and Angel One are without any doubt the worst, most embarrassing episodes of season 1, rivaled only by Code of Honor and The Neutral Zone 20th century humans storyline. I wouldn't recommend them to anyone, unless they want to be turned off from TNG for good. There's also absolutely nothing important in those episodes and they are not needed at all for understanding any of the later episodes and shows - "The Last Outpost" did introduce the Ferengi, but they were so ridiculous that the subsequent episodes had to work hard to make some sense of them. If you really want to recommend a Ferengi TNG episode, it's better to choose "The Battle", which is nothing special but isn't horrible like "The Last Outpost", and where the Ferengi aren't such ridiculous caricatures.Regarding the notorious first two seasons of TNG, I'm gonna paste below what I said in this thread started by a man who's sharing Star Trek with his wife. She was having trouble getting into the first season of TNG.
Given you've already shared numerous episodes, I won't say skip the season all together, but I do want to remind everybody that if she loses interest because of the early stinkers she'll miss both the later greatness and the early gems. And I say that as one who loves the first couple seasons.
I did a little episode ranking for myself some time back and thought I'd share, if you don't mind a list.
If you're gonna continue the first season, I say see:
103. The Naked Now
106. Where No One Has Gone Before
110. Hide And Q
115. 11001001
120. Heart of Glory
121. The Arsenal of Freedom
125. Conspiracy
If she still wants to see more of season one, consider:
105. The Last Outpost - Unless she has a low Ferengi threshhold, and who could blame her if she does?
112. The Big Goodbye
113. Datalore
114. Angel One
117. When The Bough Breaks
123. Skin of Evil
124. We'll Always Have Paris
Skip...
101./102. Encounter at Farpoint
104. Code of Honor
107. Lonely Among Us
108. Justice
109. The Battle
111. Haven
116. Too Short A Season
118. Home Soil
122. Symbiosis
126. The Neutral Zone
...until she's jonesing for any new Trek.
Similarly, for season two, I say see:
202. Where Silence Has Lease
203. Elementary, Dear Data
208. A Matter Of Honor
209. The Measure Of A Man
211. Contagion
213. Time Squared
216. Q Who
220. The Emissary
221. Peak Performance
Consider:
206. The Schizoid Man
207. Unnatural Selection
210. The Dauphin
214. The Icarus Factor
215. Pen Pals
Skip:
201. The Child
204. The Outrageous Okona
205. Loud As A Whisper
212. The Royale
217. Samaritan Snare
218. Up The Long Ladder
219. Manhunt
222. Shades Of Gray
Encounter at Farpoint is definitely one of the episodes that should be seen - not because it's great (it's not, although it's not as bad as some other episodes of season 1), but because it introduces Q and has a follow-up in many later episodes and is generally important for that reason.
There's also nothing really necessary to see in "We'll Always Have Paris". If you want to add another episode, it could be Coming of Age since it has at least a follow-up in "Conspiracy".