I think the first priority is the EPL. As for any major team from the top 4 championships. Titles in championships starting from 5th are evaluated differently and I am sure that any champion of Portugal or France would give 2-3 titles for the Champions League.
The second priority is the Champions League. This cup is valued less than the national championship, but only because this result is somewhat random.
The third priority is all other national cups and stuff, such as the club world championship. This is nothing more than a nice bonus to the main achievements, but if the main titles are lost, then such titles do not change anything.
Yup, it's true that national league champions are more prestigious than European competitions like UEL and UCL, due to domestic competition are club and fan competition with teams from cities or provinces of one country. This is what makes the domestic league rivalry more prestigious. Indeed, being at the top of Europe provides a plus for the club, but mostly UCL is the second target.
I remember a few seasons ago, if I'm not mistaken Liverpool had failed to win EPL after City managed to win in the last game. Could this be Liverpool's revenge against City in the last week of the league and get the title?