I'm going to give an answer based on my experience in the US, so it may not be applicable in other countries but:
Whether your recommenders use a generic letter is not a decision you get to make. You tell them where to send the letter, but at least in the US, you do not get to see it, and all you know about it's content is what they tell you. I would let them use their judgement about how to personalize it, though if there is something you think would particularly important at one school vs. another, it's a good idea to mention this to them.
Similarly, when they write the letter is not something you have control over. In all grad school applications I've seen, the application is electronic and the recommender directly submits via a link that's generated when you fill out your application. They'll know when the deadline is, and will probably be annoyed if you try to insist that they write their letter months before the deadline. If you're applying to a place that still uses paper, submitting the application months before the deadline when your paper application isn't there is just asking for trouble.
What does make sense is to write your recommenders now, and say "I wanted to let you know that I'll be applying for graduate school in November, and I was hoping you would be willing to write me a recommendation. I wanted to let you know relatively early since I know that by fall it will have been a while since I graduated." Don't hesitate to remind them about interactions you've had, or about anything you think would look good in the letter. Professors often have to write many such letters, and if you put your good qualities at their fingertips, they're more likely to end up in the letter.
EDIT: Looking this over, I think I could have been a little more concise. Providing your recommenders with info is a very good idea; that's why I suggest that you do email them now. They can write a better letter if they know what you plan to do and if you remind/tell them about your accomplishments, etc. But when you ask someone for a recommendation, you can't really micromanage. You need to say where the letter needs to go and when the deadline is, but there's not much else you have control over. It is unfortunate that memories fade (though they'll fade less if you give a reminder of your existence now), but that's how it goes. That's just the price you pay if you don't apply to a Ph.D. right as you finish your degree.