Do you know how people of your target language do things differently in casual text messages/on the internet?
A good example: russians often drop the double dot from smiling face )))) vs. :)))) or how in some middle-eastern languages they write hhhhhhh instead of the “hahaha”.
As someone from Europe (Poland to be more specific), I’d recommend to not worry about it. Really. Learn to say “hello”, “where’s the bathroom”, and “thank you”, the rest you’ll handle in English or use improvised sign language if the person you’re talking to doesn’t speak it (which at least in Poland gets rarer and rarer with every year). Or google translate, automatic translators work decently well for basic things.
Nobody will mind - honestly, if you were to actually learn Polish most of us would react with “that’s really impressive but why bother???” You’ll get the same reaction in most other countries except for maybe Spain/Germany/France, they’ll be more used to people knowing their languages, but at least in Germany they’ll still probably try to talk to you in English.
Of course if you want to learn for fun then go ahead, but there’s no need to put too much pressure on yourself, I’ve been all over Europe knowing only English, Polish and how to read cyrillic script and it was more than enough. English gets you 90% of the way there.
I don’t know what specific countries you’ll be going through, but focusing on French (if going through France), German (in Germany + a bunch of neighbouring countries + a lot of old people who don’t speak English in Western Europe will know it), and some slavic language (probably Polish and/or Russian, Polish will get you through Poland and with effort through Czech Republic, Slovakia, and parts of Ukraine, Russian is useful because, as with German in Western Europe, a lot of older people in former Soviet republics will speak it, but bear in mind it has some negative connotations) should cover the basics.
If you have any questions feel free to message me!