You will be emotionally attached to the characters one way or the other, but it may not always be positive. There is one character, Owen, the fellow with the spray who you are ABSOLUTELY meant to hate. They set it up for you to hate him...he's an irredeemable prick and you don't understand why anyone likes him...and later they redeem him, but there is a lot of hate to come first and a lot of fans that think the redemption or excuse really, is too little too late, if you stick to watching you can decide for yourself. I think whether we have a positive or negative reaction to stories and characters the fact that we are so passionate about it speaks to the quality of the writing.
And there are a lot of characters you will love! Gwen is 50/50 some love her some hate her and I think that's the fine line between relateable and outright stupid- no not stupid - impulsive. But then you have Jack, Ianto and Tosh and a number of guest characters and you will fall in love with them. You will care about their stories and their various tortured relationships. A lot of fans jokingly call the show "Torturewood" because it's pretty heavy emotionally at times. You will love it. I have no doubt of that.
Give it 'til episode 4. Episode 4 is a beautifully done, emotional slap in the face of an episode written by Chris Chibnall who is always stellar. Now it's time for my bit of blasphemy - I love Torchwood more than I love Doctor Who - and I love Doctor Who a lot. I hope you keep going I'll be interested to hear what you think.