Go modular, network, maybe even look at an ops job whilst you train.
Also, you may want to fly a shiny jet (as someone who has flown both the aircraft you mention, the 737 will teach you a very solid jet pilot skillset but on a busy 3 or 4 sector day it is the bus every single time for me!) but there is nothing wrong with a solid turboprop job - it will make you a very good pilot indeed. If what you are interested in in aviation, then ANY flying job should be your aim. If you want to “live the dream” that social media sells then you are in for a bit of a shock.
At the moment DEPs at BA for example are from a huge wealth of different backgrounds; some from EZY etc for sure but also people from Blue Islands, Aurigny, Loganair, West Atlantic, Titan, Corporate aviation…. modular and integrated are both represented. Someone who joins BA mainline with a few thousand ATR hours after spending 64k on modular training and having their type rating paid for by the likes of BI will be better off than someone who splurges 100k on an integrated course and then 30k to a blue and yellow airline…. No matter what instagram or TikTok say.
Tagged simply means you are on an integrated course but have a conditional offer from someone like EZY at the end. Generally self sponsored.