hmm, this is tricky to tackle
Do you plan to subscribe to gamepass? if the answer is yes, then get ally x or xbox ally
If you have no interest in gamepass, then go wtih Steam Deck or Legion GO S. The Legion Go S runs on the Steam OS, and it will give you better performance than the steam deck
1st gen ally is an ice device you can get for cheap, but the major drawback is battery life and that won't fit the use case you mentioned above.
Overall, You might be best off going with Ally X because it has improved battery life, good performance, and gives you easy access to gamepass, steam, epic game store, and other storefronts. If you don't care about flexibility between store fronts then Legion Go S might be a good bet, but price-wise most likely better off going with a steam deck.