The OE woofers are 5.25". The tweeter size for replacements vary by brand. Search Youtube for e39+speaker+installation and you will find various videos by BSW for speaker replacement DIY. I would also search this forum for some more background info. You don't specify type of music you prefer nor the volume level you typically use. Here's a quick synopsis:
1. Priority 1 - Replace your front door speakers with a high quality 2 way system. This will make an audible difference in sound clarity and definition.
2. Rainbow is probably the top end in terms of quality but they are also the costliest. Many good alternative options (Infinity, Boston Acoustics, etc.) exist for less than $125-$200/set.
3. Priority 2 - Installed a powered subwoofer before spending your money on rear door or rear deck speakers. Replacing these other speakers makes a minimal improvement in overall audible sound quality. The low end is the missing link in the e39 audio system and must be addressed.
4. Low end options include powered rear armrest subwoofers for less than $200 (do a search for the DIY). The sky (and the budget needed) is the limit for high end.
5. Unless you like REALLY LOUD music, the OE amp is adequate for casual listening.
6. The head unit is adequate unless it lacks specific features (nav, aux input, etc.) you are seeking. Keep in mind you may sacrifice some utility (access to OBC) if you replace the HU.
7. If you need an aux or iPod input, there are multiple options (Dice, Intravee, etc.) available. Do a search for more info.
Keep in mind audio quality and what is needed to attaiin it are highly subjective so you will get multiple opinions on this matter. My personal opinion is tempered by maximizing return on investment. Enjoy your ride.