I think social welfare is generally a positive thing for society - nobody should have to starve, become homeless or sacrifice their retirement savings due to circumstances beyond their control (such as losing their job). However, it is also important to not destroy the incentive to work - we should balance the aim of having everyone contribute usefully to society with the safety net. It seems the UK isn't doing a very good job with this at the moment as there are people on welfare who could work and would like to except that it would mean having less money for greater effort (a minimum wage job pays less than welfare, and if you have the job you stop getting the welfare). There are also many teenage girls who become pregnant just so that they will get a council house. [EDIT: This is an unsubstantiated and almost certainly false claim - I heard it on the Jeremy Vine show and failed to research it before repeating it here.]
If we were designing the system from scratch, one question might be to ask "what do we do with someone who is just Terminally Lazy (TL)?" I.e. what do we do with somebody who simply refuses to work or contribute to society at all? What sort of lifestyle should they have? For humanitarian reasons, I don't think we should let them freeze to death in the streets, so I think they should have some sort of Basic Minimum Standard Of Living (BMSOL). We would also like to avoid the possibility of them committing crimes simply so they get sent to prison and have a place to sleep (on the general principle that encouraging crimes is a bad idea). I also don't think we should treat TL-ness as a crime itself - if a TL person wakes up one day and decides to go and get a job and become a productive member of society, that should be encouraged - they should not lose the ability to do that.
I think that the concept of "prison" is the right idea here, though - apart from the "freedom to leave" thing, there is no reason to provide any better BMSOL to a TL person than to a convicted criminal. In both cases, we only provide that BMSOL for humanitarian reasons. Let anyone who wants to have a bed for the night in conditions that are roughly the same as those in prison: shelter, a bed, basic hygiene facilities, up to three square meals per day and a basic level of medical care. No sex, booze, drugs or TV.
Paying for the BMSOL for the TL whilst making the non-TL pay for those things isn't exactly fair, though, so let's have a guaranteed minimum income (equal to the cost of the BMSOL) for everyone, and give people the choice of receiving it in the form of cash or BMSOL (or some of each).
If you want more than the BMSOL you have to do some work. With the BMSOL system in place, the minimum wage could be scrapped which would mean there would be plenty of work to go around (the problem with unemployment isn't that there's a lack of stuff to do, it's that because of the minimum wage there's a lack of money to pay people to do it).
How to pay for all this? I tend to favour an income tax since it's cheaper to collect and more progressive than a sales tax. I think inheritance tax is one of the most fair taxes, as I've mentioned here before. Seignorage (if carefully controlled) is probably also a good idea. It would be nice if the government had a national surplus rather than a national debt, so that it could make some money from investments rather than having to pay interest. Sin taxes (on booze, tobacco, recreational drugs, pollution and gambling) should be levied exactly as much as necessary to undo the harm that they cause (so smokers should pay the costs of treatment of smoking related diseases, etc) - any less leads to the abstinent paying for the sins of the partakers, and any more could lead to encouragement of the sins.
Income tax should be calculated as a function yielding 
- There is always an incentive to earn more (i.e. an increase in your salary always corresponds to an increase in your take-home pay) -
.
- The tax is progressive (i.e. the more you earn the less of your salary you take home):
.
- There's no tax on the first penny (i.e.
at
).
- A minimum income is guaranteed (i.e.
) rather than a minimum wage (
).
Because the minimum income is part of the income tax system, the tax bill 
It would be interesting to write a program to simulate the economics of a society and see what effect various tax and welfare schemes have.
Edit 14th July 2013:
[...] said before that I would prefer to replace the minimum wage with a guaranteed minimum income, but I've since [...]
[...] particular, I had always thought that income taxes were the best kind of taxes, being progressive and cheap to collect. However, as Planet Money [...]
[…] the supply of housing is insufficient for the people needing it. For these circumstances I think a basic minimum standard of social housing would be a necessary fallback when there's nowhere else to go. As a general rule people would not […]