Learn Hardcore Chinese: wǒ xiǎng qù chāoshì huòzhě zài jiā chī wǎnfàn. - I want to go to the supermarket or eat dinner at home.

Use 或者 in statements: it links alternatives when you’re simply stating possibilities.
- 我想去超市或者在家吃晚饭。
Use 还是 in questions to offer a choice:
- 你想去超市还是在家吃晚饭？
In statements, 还是 usually means “had better/rather/after all” (not “or”):
- 我们还是在家吃晚饭吧。 (Let’s just eat at home.)

Do the two options have to be the same “type” of phrase? One is 去超市 (go somewhere) and the other is 在家吃晚饭 (do something at a place).

They don’t have to be perfectly parallel; everyday speech often mixes types. If you want tighter symmetry, you can say:

Why is 在家 placed before 吃? Could I say 吃晚饭在家?

Location phrases with 在 + place typically come before the verb to indicate where the action happens:

Why don’t we say 在超市 after 去? Why is it 去超市, not 去在超市?

去 + place expresses movement to a destination: 去超市.
在 + place marks where an action takes place: 在超市买东西. You can combine them if you also include an action after you arrive:
去超市买东西 (go to the supermarket to buy things)
我打算在超市买菜 (I plan to buy groceries at the supermarket)

What nuance does 想 (xiǎng) add? Is it “want,” “would like,” or “think”?

Here 想 means “would like to / feel like / intend to,” which is softer than a firm decision. It can also mean “to think” when followed by a clause:

How do 想, 想要, 要, 打算, and 会 differ?

想: mild desire/intention (“would like to”).
想要: desire with a bit more emphasis; often used with nouns; with verbs it’s common in Taiwan, less needed in Mainland speech.
- 我想要一杯咖啡。/ 我想要去超市。(OK, latter more TW-feel)
要: strong intent/plan (“going to/plan to”).
- 我今天要去超市。
打算: having a plan (“plan to”).
- 我打算在家吃晚饭。
会: likelihood/ability (“will / be likely to”).
- 我今晚会在家吃。

Can 我想 mean “I think” here?

Not in this sentence. 我想 means “I’d like to” because it’s followed by an action (去…). To mean “I think,” it should introduce a clause:

Is 在家 the same as 在家里? Which is more natural?

Both are fine:

在家 is very common and slightly more concise/colloquial.
在家里 can feel a touch more explicit (literally “inside the home”). Meaning is the same in most contexts.

What’s the difference between 晚饭, 晚餐, and 吃饭?

晚饭: dinner; very common in Mainland speech.
晚餐: dinner; a bit more formal/common in Taiwan; also used in ads/menus.
吃饭: to have a meal (any meal) or “to eat” in general; context decides which meal.

How do I turn this into a choice question to someone else?

Use 还是:

How do I make it clear it’s strictly one or the other?

Use 要么…要么… (either…or…):

Any tips to sound natural if I mean “just pop to the supermarket quickly”?

Use a “trip” measure word or 一下:

我想去趟超市。/ 我想去一趟超市。 (a/one trip)
我想去一下超市。 (go for a bit) All are common; 趟 highlights “a trip,” 一下 softens the action.

Pronunciation: any tone-sandhi I should watch out for?

我想: two 3rd tones in a row; 我 becomes rising in speech: wó xiǎng.
去 qù (4th), 超市 chāoshì (1st–4th), 或者 huòzhě (4th–3rd), 在 zài (4th), 家 jiā (1st), 吃 chī (1st), 晚饭 wǎnfàn (3rd–4th). Say it smoothly as: wó xiǎng qù chāoshì huòzhě zài jiā chī wǎnfàn.

Should there be a comma before 或者?

It’s optional and depends on your intended pause:

Do I need a measure word with 超市?

Not when it’s a general destination: 去超市. If you specify one, use a classifier like 家 (common for shops/businesses):

Where do time words go, like “tonight” (今天晚上/今晚)?

Common placements:

Could both actions happen, or does 或者 imply only one?

或者 itself is neutral (“or” in statements); context often implies you’ll choose one. If you want to allow for both, say so explicitly:

我想去超市，然后在家吃晚饭。 (first A, then B) If you want to force a single choice, use 要么…要么….