Sorry to hear about your situation.
We can't give legal advice online, only information, so I can't advise you what Chapter to file but I can tell you some information about each.
First of all, Chapter 7
discharges debts and the court liquidates property which is in excess of the amount you are allowed to exempt (i.e. protect and keep). Chapter 13 is a payment plan where you pay all or a portion of your debt, depending on how much you can afford.
An advantage (and disadvantage) of Chapter 13 would be that it would cure your tax situation. I say advantage, because if you pay taxes through a Chapter 13 Plan, they can't charge you any more penalties or interest. I say disadvantage, because the tax liability has to be paid off by the end of your 5 year Chapter 13 Plan, which may not be feasible.
Chapter 7 would not require you to pay the taxes right now, so you could discharge the other debts and then set up payments on the taxes, but would not stop penalties and interest on those taxes.
Another consideration is your stock in the LLC/corp. Some states consider stock to be a cash asset, in which case the stock would not necessarily be exempt (safe) in Chapter 7. So, if you file ChapterXXXXXmay make you liquidate your stock and give the proceeds to creditors. In Chapter 13, you could probably keep the stock even if it is not exempt as long as you set up your Plan to pay the reasonable value of the liquidation value of the stock to unsecured creditors over the 5 year Plan. If the stock has no value then this may be a non-issue, but you will need an attorney to review taxes and other documents to make that determination.
Chapter 13, but not
Chapter 7, can also allow you to strip (i.e. wipe out) a wholly unsecured second mortgage, so if that is the case, the scales may tip that direction somewhat.
I suggest you consult with an attorney since your situation could have a lot of pitfalls and complications.
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