What are the financial ramifications for buying a house under my LLC

It sounds like you just want to buy an umbrella policy to cover whatever taxable assets you hold.

If you hold your primary home in a LLC, you personally hold 100% of the shares of that LLC, and you are sued for personal negligence, your LLC shares are an asset that can be seized to pay any judgement. $100,000 in shares of Your New LLC are no different than $100,000 in shares of Apple in a taxable account in this case.

In most states, it's actually worse than that. Most states have a homestead exemption that allows you to avoid selling a primary home up to some reasonably high value to satisfy a creditor. You'd lose the homestead exemption if the home was owned by the LLC rather than you.

And as a cherry on top, in order to avoid piercing the veil and making the LLC useless, you'd need to pay rent to the LLC for living in the home which would be taxable income for the LLC and wouldn't be deductible for you so you'd end up sending Uncle Sam a decent chunk of change for the privilege of getting less of the protection from lawsuit that you're looking for.

A very wealthy person that owns a number of properties may hold them in a bunch of different LLCs for a variety of reasons. If you're a large landlord, for example, you may want LLCs for each property so that if something happens at one property that causes a lawsuit against the property owner LLC, the worst that happens is the LLC files for bankruptcy and sells of that one property to pay the judgement. If you have 10 properties and a tenant in property 1 sues, you don't want to have to potentially liquidate the other 9 properties to pay the judgement. If the landlord in this example was sued personally, all 10 properties could be liquidated to pay any judgement (or, more accurately, the landlord's shares of the 10 LLC's could be liquidated to pay any judgement). If only the property 1 LLC was sued, only that LLC's assets could be used to pay any judgement.