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There's probably no perfect solution, but some form of PR, probably STV, would be my preference. It's more democratic than FPTP, and it is also unlikely that extreme parties would get many 2nd pref votes. Can't say I don't like the idea of everybody voting, but not sure I could stretch to making it compulsory! I still get a slight thrill from voting (although usually followed by bitter disappointment).
How would you solve that then? Endless hung/NOC Parliaments or huge coalitions that argue amongst themselves and self destruct in short time? AV/AV+/STV or a hybrid such as MMP/AMS?
Personally I'd like to see the UK aim to move towards some form of PR and compulsory voting, but I can't say that I'm not worried about what the majority of the population might end up electing if compulsory voting was enforced under FPTP.