Hello, friend. Let me start my reply by saying that im not presenting any of this as judgement, im sitting here wishing I could send these thoughts back to a younger me, because I remember the gut wrenching nights just trying to get these images out of my head. Im also a rambler, so yeah, long post coming...
Off the top let me say that theres nothing wrong with feeling this way, it doesnt mean that youre a bad guy, but how you view it and how you react is critical in the "dont be an asshole" department.
Youre new at this and youre a work in progress.
First, realize that this is not how the rest of your life will feel, but the issue is not going to go away. Every girl you meet will have a past and pursuing a "pure" woman is a fruitless task that will make you bitter and keep you from growing as a person. Its not "old fashioned", its small minded and unrealistic, and when it was the norm it was because men were trying to control womens choices and not face reality.
You will never enjoy the mental image of your partner with another man. I dont. But what ive learned is that this feeling is really just my own insecurity. Just like any other negative thought, its not optional but you can learn to accept that its not based on reality really, or you can wallow in it and let it eat at you every second. Its a process to learn to live with your insecurity, part of learning how to be a man.
Now the important part. A mature man (or woman) doesnt put the weight of their insecurity on their partner. She didnt do anything wrong, her past is not about you. You say that you feel like she is "ruined in a way", and as someone who faced that feeling I will tell you that you are starting down a road where you will cause this person and others (when you burn this relationship to the ground and move on) a great deal of pain. YOU will be the asshole, my friend.
You put it under the guise of concern for her having to live with "always having the memory" of him. This is incorrect. You have the burden of his memory, she had an experience she learned and grew from, that is over now and she is happy to be past. Your burden is not as heavy as it seems now, its the same one we all face, but if you put it on her as though she's "tainted" youll fuck up your relationship and her own self-esteem. Thats selfish and helps no one.
Want to be a good dude and give this relationship a real chance? Communicate that youre feeling insecure, not because of the specifics, but because youre new at this and exes, any exes, are hard to not feel jealous over (and it IS jealousy.) But tell her that you care about the present, about the person she is and your possible future. And mean it.
Just the opinion of a more experienced guy who cringes more thinking about the girls ive made cry than over imagining my partner with someone else in the past. I have the thought once in a while, it passes, I go and tell her how much I love her more every day. Shes really the best and Im grateful for whatever past led her to me.