Regarding ME time, I bought some (safety pilot) until I could qualify to MEI (insurance). I had a total of 350 ME when I got my first airline job.

At the time you needed close to 2000 hours to get an interview, so I had PLENTY of time to network and do the odd ME student at the FBO. In today's environment I suspect that you might not want to delay your airline job for two years while you scrounge ME time...I'd probably just buy a block.

In the distant past, some airlines supposdly did not like SP time, but I don't know of any that specify that today. If in doubt contact the airlines you are interested in and ask. It should be obvious that an airline would choose an MEI or 135 pilot over a safety pilot if they had to make a choice, but today they can't be picky.