Also would it be better to put me down as the main name on the claims?
I'm assuming you are a British citizen or you have ILR too.
The Tax Credits claim
must be in both names. You cannot claim to be single when you have a parter as the partner's salary is used in the calculations.
You could have claimed before your wife had ILR. It wouldn't even have mattered if you had got extra WTC for your wife even though she wasn't allowed public funds, as you have a child. For Tax Credits, if you have a child and one person is allowed public funds, then the claim is treated as neither being under immigration control. That seems to be changing when Tax Credits is replaced by Universal Credit. As per the budget, be aware that the Tax Credits benefits are getting reduced from April 2016.
Child Benefit can be in either names as your wife has ILR. You should have claimed this before and just put it in your name as a British citizen is allowed to claim. If your wife is earning enough to pay her National Insurance then you might want to put it in your name if you are worried about the future of your ESA as receiving CB gives a credit for national insurance and therefore state pension. I'm sure you are aware that starting from next year state pensions will only be based and our own contributions.
If your wife is earning 50k+ then this will reduce the CB. About a 60k salary will stop the Child Benefit unless she can reduce this by paying more into her private pension, or you can choose to take the CB for the NIC credit towards state pension and then your wife will need to self declare to HMRC each year to pay the money part back.
I hope that makes sense.