Considering crystal and service

I recently acquired this 1970 Geneve with 613 movement through eBay on a second chance bid. The original purchaser returned it, according to the seller, because it was running fast two minutes per day; I was second highest bid. I took a chance on it because I thought I could learn from it. Well, it seems it is losing about 15 sec/day. Maybe the purchaser didn't like the scratch on the crystal that wasn't obvious in the listing (https://www.ebay.com/itm/374257562823).
My taking a chance was in part because I had been looking for a vintage Omega manual mechanical, and thought I could learn from it. I feel competent to replace the crystal and adjust if needed; 15 sec/day might not be worth the trouble. The calendar, with push-pull date change, works, it keeps pretty good time by my amateur reckoning. Is this a good starter watch in my own amateur learning space, including maybe clean and lube? It would be my first on a watch of this quality and sophistication. Your advice, tear down or not, pick a different one, whatever, would be appreciated. After all, some of you helped me buy it in the Recommended Vintage thread a couple of weeks ago. So what would you need to know about my experience, tools, outlook?
Best,
Del

The pros will weigh in soon, but if you want to try working on watches, start with Russian/Soviet pocket watches. Plentiful, and a lot of those sellers are in Ukraine, so giving them a few extra dollars is a kind thing.

Doesn't hurt that they are dirt cheap.

As tools, my watchmaker said that Bergeon are the best. I am not an watchmaker so I said only what I heard.

Thanks much to you and others. I will take your sound advice
Best,
Del

But I might replace the crystal. I like the idea of doing as much as I can. I have replaced plex crystals on other watches, and I can take the movement out of the case for its safety. Any tips or pitfalls here? I have the crystal for this case, a 5005.
Best,
Del