Deposit: Depending on where you live and where you want to buy. People here tend to buy in the suburbs unless they're 'moneyed' (heirs, heiresses, lottery winners, royalty, senior civil servants), in which case they can buy outright. You usually have to save from when you get your first pocket money these days ('Don't buy a lollipop/choccy bar darling, put it towards the deposit on your bijou - size of a dog kennel - residence)!
Budget: stay within it and if you go for an older house/flat make sure you've got the cash for modifications and repairs.
Improvements/Modifications: Don't embark on any until you've read the small print. Over here we have all manner of restrictions for the outside appearance of property. If you live in an 'area of outstanding beauty', in a national park, in a Grade I or Grade II listed building or in a borough with an unusually tough outlook on external changes then I can only say: 'forget it'. You're lumbered with what other people will allow and you're severely restricted as to what materials you can use to restore your property. And if you're thinking of outside swimming pools, DON'T!
You can buy property at auction, but the cheaper it is for the size of the property the more work will be involved (that's that castle in the Highlands scotched for a start)!
With regards apartments, there are charges for the upkeep in a block of managed apartments etc, and there are other (usually hidden) charges such as when the landlord upgrades the roof or replaces windows, doors etc.
Buying property can be a minefield. Best buy a mine detector with your property!