I am designing my personal FM receiver, and I have a question regarding how to design my Antenna, in terms of choosing the wavelength to determine the size of the antenna. To put it as simple as possible , how do I select my the length such that it can detect 88-108MHz?
You probably know that antennas only resonate at one specific frequency, and that's usually where they work the best. However, they will still work at slightly lower and higher frequencies, just a little bit less well (lower/higher impedance, less gain, etc).
In your case, since you're trying to receive, the change in impedance is less of a problem for you, and since FM stations (usually) have pretty strong signals and your antenna isn't likely to be built for a high gain anyway, both of the above issues aren't going to affect you very much. My advice would be to cut your antenna for the middle of the FM band and not to worry about having it not resonate at all frequencies of the FM band.