Combat:
Avoid any combat at first. You are weak and don't have the guns or crew to manage it. There will be a time later when you are strong, but this is not that time.

Party Comp:
Dump Finnegan because he has no quests and find a better party member. I recommend you actually get a fresh compliment of crew if you can afford it through the 10G set out a poster option. They will give you better stats which are helpful early on and they will provide quest opportunities to get you apprehensions. Keep Rutherford and Tybalt from the original crew. Rutherford's quest is the easiest to finish and offers a decent payof for starting players. Tybalt's quest requires you to get into combat at least twice. The first time any encounter is okay, but the second time it will be a skill challenge. Try to make this happen before arriving back to the city of keys for the first time. His quest is easy and once it completes, he offers a nice reward of restoring sanity.

Searching:
It doesn't matter where you start exploring first too much, however you should not go too far west or south yet. I recommend searching east and then circling up north. The quests there are decent and a good place to cut your teeth. Pay attention to the Founders Fire and be on the lookout for good deals on Cannons. We will come back here later. While looking for cities, ALWAYS look into the houses and the wells. Whenever possible, try to stock up on glimpses of another world, which these events get you. NEVER sell these or trade them away until you find Ghoulwatch.

Leveling:
Dump as many stat boosts into Esoterica as possible. It gives you more apprehensions and will make leveling much easier. It is also a useful skill for knowledge checks. After Esoterica, Guile is great to level, as it helps you escape battles before they start. Insight can also be good to help you find new cities, but those two are the main ones.

By now, you might feel you are ready to explore further in the house. You survived a few trips out of the city of keys and have seen some new places. At this point, you may be ready to start buying better equipment or trading.

City of Keys:
Always work on magnum opus if possible and poetry, these are easy apprehensions. If you can get lurid tales and thrilling yarns, do it, this is good money. Pick one journal to deliver news to and devote yourself to it entirely, as they will give you bonuses later down the road. Open up your museum. Whatever you donate, the percentage will go up, but be warned, if you put evil or creepy things, you gain good stats, but lose out on money and a good reward further down the road. Be wary. Buy fuel, but do not buy fetch mirrors, (unless you have none, you want at least one) or cannons, but feel free to upgrade your engine here or elsewhere if you can afford it. When you have around 5000G, you are almost ready for combat and to become unstoppable.

Upgrading your Kinetopede:
You should not be running out of space yet, but if you need more and have 950 more than the 5000 you need, dump it on a spare car, that will give you another 50 space. Go to Founder's Fire and spend about 2000G on their armor, this will take you almost to 200 health. Go to the city of knives and buy their cannons. They are about 900G a piece. Get three. They are moderately strong and have good accuracy. Having four cannons and four gunners will make you a formiddable force in combat. Make sure you have four gunners, however having four of each lower crew member is great for the stat boosts and defenses against boarding.

Combat:
Focus down individual guns to reduce the damage you take. When one gun is out of HP, move on to another one. Four guns means four shots and the city of angel guns are strong and accurate. City of Bridges offers bounties which pay out nicely and if you have Genieve, you can take bounties hunting vampires.

Leveling up:
If Esoterica is high enough, focus on Insight, Guile, Guts, and Vigilance. These are some of the most common challenges you will face and they will help you not die on some of the more dangerous challenges. So far, graft is the least used skill, but do not neglect it too much.

When you are comfortable, head west. Be on the lookout for Ghoulwatch. Remember Ghoulwatch. You should be able to speak to the Silent Minister and trade for items. You get paid less than other cities, but remember the glimpses of another world I told you to horde? You can trade them for 90G and a fetch mirror. Fetch mirrors can be sold for 200G a pop, making this easily the best way to make money via trade and keep a strong supply of fetch mirrors handy. Do not eat the food. Continue north and look for Chaga and Azorim, they are good for finding rare items with the previously mentioned skill challenges. What you want to find is Icicle peak, however. This will let you buy kinetopede treads that are not slowed by snow or swamp to the south, basically allowing you to explore at your leisure. Fetch mirrors from Ghoulwatch also make fast travel easy now too. This should make traversing the house much simpler.

Congrats! Now you are ready for some of the crazier challenges the house has for you. Before I leave you, some random tips:
Zero sanity shop:
At some shops if your sanity is very low, you can buy unusual curios. Oscillating prisms are cheap here and useful for your museum and for several quests. Bear this in mind.
Zero sanity:
Strange events will happen at zero sanity, but it does not instant kill you, so do not be too afraid to go low. Also, you cannot recover sanity in the city of keys with a month off unless your sanity is low enough, be aware.
Portentous dreams:
Your get out of jail free cards. Hold onto these if you can. Don't be afraid to spend them, but if you meet with gods or demons, they may save you. Use as a last resort.
Doors:
In the southern part of the house, you will start seeing locked areas. You need a super rare key to open any of these, however the only ones you can open have a glow around them. They lead to interesting places.
Save scum:
Do not be afraid to save scum before making choices. You can save scum to get more interactions at cities, but I do not recommend this as it breaks the flow of the game. However, you can save, this is not a rogue-like, save before you make a scary choice and if all your crew are dead by the end of it, reload. This is nothing to be ashamed of, you are here to have fun. Not all choices are clear, either.
Minor Trade Routes:
Angel wine from city of angels to the Blue court gets a nice return of 10-40 per depending on where you buy from.
Arms shipments from anywhere, there are many places selling them, to City of bridges nets 10-60 per, depending on where you buy from.
Laudnam can be bought at Fargyle and sold at City of Masks at a 10-20 markup, one of the easiest early markups.
Items to save:
Occult relics, bottled darkness, oscillating prisms, keys, undreamt treasures, angel wine 79 vinatage. These are all really rare items and are instrumental on many quests. There are ways to find them, but they are tedious and much more random than other items, so hold onto at least a few if you can. It's wise to hold onto 1 of any item you have because many trigger quests with your crew or other cities, but your hold space is limited, so make your best judgment.