MPs should certainly have a higher basic salary. You could argue that people should enter politics out of a sense of duty or vocation - and therefore they should be paid like charity workers or priests! - but who's going to take on that much grief for a pittance? No one should be going into politics because it pays well, but on the other hand it's a hugely responsible job (if they do it properly) and should be adequately rewarded.
But even if they did have a higher salary, there have to be some expense claims - if you have a Cabinet or ministerial post and need to travel abroad, for example, you can't be expected to pay for your own flights and accommodation. No-one in an ordinary job would do that.
The existing rules shouldn't really need much changing if they were actually applied properly. MPs are only supposed to be able to reclaim expenses incurred "wholly, exclusively and necessarily" in performing their duties.... but clearly that test hasn't been applied in practice!!
The big problem is the second home allowance - they're entitled to claim up to about £23,000 a year and the culture basically seems to be to claim it as a matter of course, as if it's additional salary. Added to that, MPs are obviously playing the system by deciding which home to nominate as their "second" home, in order to get the maximum benefit. I don't know how they're going to get round that.