I hope the flats not rented as the landlord won't be best please to find a "workshop" on your balcony. Also I don't thick your neighbours would be happy with all the wood shavings falling on their balcony. I'm not saving don't do it, just give it some thought on if it will affect anyone else. Might save some issues in the long term.
However, if you still want to go through with it any metal vice would be good, just make sure it has an opening bigger than 120mm. Prob best checking you you have enough working room first before making any alterations or buying any tools.