Fed up with problems of Multibit HD now (have to restore back to the first backup every time I have to open my wallet, otherwise password does not work) I've decided to move to another desktop wallet.
For now I'm considering Electrum, is this the best choice? Please suggest.
And secondly, what is the best and quickest way to move my coins from one wallet to another?
I've been using electrum for years without a hitch... I would consider it secure and easy to use.
The easyest way to move your coins would be to create one single transaction using your multibit HD spending all unspent outputs as an input and only generating one output that can be spent by the first address of your new electrum wallet.
In other words: create a new, clean electrum wallet, generate a payment request, then withdraw everything in your multibit HD to this electrum-generated address... Since it's a transaction between two wallets you own, you can cheap out on the fees a little bit
BTW: don't discard the recovery seed phrase of your multibit HD, it's a good habit never to throw away these things...