I think you really need to narrow down where you want to live and how much a house that would fit your needs costs in that area first.

You can buy an awesome cheap house in the middle of nowhere and you’ll hate it because there’s nothing to do. Eventually you do have to go outside and make friends and if you don’t like your area, you’re stuck

Anything less than the standard of 20% will incur an extra PMI charge (on top of borrowing more money). The PMI is a percentage of the price, but the % value varies across lenders; so you’ll just have to ask and see what you’d get offered (note that you can request for this PMI to be removed once you hit a % equity ownership, usually 20%; but there may not be a legal obligation for them to drop it). The interest rate you get would also of course be a huge factor.

American northeast; so let's say NY, NJ, Connecticut, new Hampshire, Rhode island, Maryland and Delaware, and the farther north states (which I haven't looked for housing in so have no input). Delaware is probably the cheapest, and has cheap tax, but it sucks. NJ is crowded and expensive but has some really great towns that you def can't afford to live in for $150k. 500k at least. Rural NY has some great, cheap old farmhouses and older homes that you can get for 150k, so your 30k is already enough. The taxes are high, but water is cheap, clean, and plentiful and the land is good. In Pennsylvania the taxes are cheaper. Farms and land is expensive, but you can find cheaper houses in old slate mining towns and blue collar cities. Some of them are run down, but some like Bethlehem are thriving and would be a great place to live to be close to "stuff" but not in the city. For a true city, I'd look at Baltimore, Maryland, where you might be able to get a townhouse for 200k or less, for now. Who knows what the market will be in 3 years.

Really going to depend on the price you're willing to spend on the house. I like to target 20% down on a house. For savings, a HYSA would be the best option. If you can find a 1-2 year CD that's higher that would be fine but you're not talking about a lot of difference in increase of principal.

If you don't put like 20% down the underwriter will almost assuredly required you add Mortgage Insurance ontop https://en.wikipedia.org/wiki/Mortgage_insurance which just adds more fees and to escrow

If your target house is $150k, then your 30k will allow you to avoid PMI (mortgage insurance). If a higher target price for the house, try to save more. Getting to 20% down should be a must. PMI is money you typically never get back and with 20% down, it can be avoided all together.

I put 0 down and I used that money to invest and keep as a safety net. I've made more back than if I shelled it out up front.