Yes, both are good ways to achieve bilingualism. There isn't one universal best way, since things vary a lot from one family to the next.
The following assumes you're raising your kids in Germany, since that's what you implied.
Scenario 1: Your fiancee speaks English to the child, you speak German.
> The child will start learning both languages from birth.
> You will be more comfortable since you're speaking your native language.
> It will be more work to get the child sufficient English input. If you have English-speaking preschools where you live, that would be a very good idea.
> If the mother understands German and doesn't stick to strict English-only communication (e.g. child speaks German, mother replies in English), the child may grow up to understand English but be unable to speak it (passive speaker).
Scenario 2: Both you and your fiancee speak only English at home.
> Your child will get much more English input (it would still be a good idea to seek out other sources of it though).
> Your child will still attain native(-like) competence in German, although it will happen later. German will ultimately be the child's dominant language both in scenario 1 and scenario 2.
> Your child has a better chance of attaining a higher level of competence in English, and a better chance of maintaining it.
> You will have to speak your non-native language at home, which for some people may make them feel like it affects their relationship with their child.
> Your child's knowledge of German will be behind that of their peers until they catch up. In this scenario, I would recommend getting the child out into the community starting from a younger age than you might otherwise. I would recommend sending them to a German-speaking preschool so they have more exposure to German and more practice speaking German prior to entering elementary school.
> During the first few years of life, the child might not know enough German to communicate with German-speaking relatives. This will change fairly quickly once the child starts preschool/school.
Both scenarios have their pros and cons, and there may be more pros/cons that I've not thought of. One way isn't necessarily better than the other, it's just up to you and your fiancee to decide which way you like best. The most important thing is that you're consistent, and you choose a plan that you know you both can stick to.
It's good that you have a lot of time to think about it and decide. I'm sure there are some "language acquisition for parents" type of books that go more in-depth, so I'd encourage you to take your time and do some more reading. I'd recommend you a book but unfortunately I haven't personally read any (I'm not a parent, I've just studied linguistics).