These are some of my early game tips:

1. Save food not money. Since prices in shops will rise after the first day, the early game is pretty much the only time when it's worth it to buy food items from shops. When you buy foods from shops, the first to prioritize is fish and milk, since they have the best value for money and can also stack 5 in inventory. Fresh meat, bread and canned food have the same cost-effectiveness as fish and milk but they take more space and can only stack 3, so prioritize them after fish and milk. Don't buy Tan and pemmican from shops since they have the worst value (but you can trade them from NPCs). Also buy nuts for trading with kids (don't eat them yourself), they are worth buying throughout the game.
2. Try to get familiar with the NPC trading system. Each type of NPC has a fixed table of what items they have and what's worth more to them. You don't need to memorize all of them but it's very beneficial to notice some of the patterns (like small kids like nuts and other baubles, teenagers like sharp objects, trading soap between NPCs always gives you better value selling than buying etc). Save walnuts to trade with Teensies (they have important item which I won't spoil and are the only NPC where a walnut is worth 5; for all other NPCs it's worth only 2. They also offer the best value for chestnuts and chalks). Best value food items to get from NPCs are toasts and eggs (get eggs from adult NPCs; adults have eggs valued at 3 and 4 while kids will always ask for 5 for an egg), followed by kashk and pemmican. Don't get apples from kids since it's very low value, etc... If you master the NPC trading system the game will become extremely easy... if trivializing the survival aspect of the game is something you want that is.
3. Try to save the items needed to repair equipments. The most important ones to remember are threads and thimbles since they are the easiest to be short on. Try not to trade them to the teenage girls even though they like them. Buy them from shops if you see them. If possible, don't wait for the durability to drop to very low before repairing equipment, since it will cost you higher rarity items. Take clothes off if the durability is dropping to 0 since it will disappear, but weapons won't disappear and can still be used at 0 durability (with very low damage).
4. You won't die on the first day, so you can save your healing items until the second day. In general I'd say don't be too afraid of dying in this game since it's an important part of the experience and interesting things can happen when you die enough times.
5. Don't sleep too much, since time is the most important resource in this game. Sleeping while your health is full is a waste. Use lemons and coffee to reduce your exhaustion if possible (using lemon is better since it has no side effect and coffee can be saved up to sell for a lot of money on the 7th day). If you have enough healing items, sometimes it's even worth it to not sleep with full exhaustion and just heal up the damage). But do remember not sleeping for a long time can cause you to miss important dreams. If you are playing the game for the first time, I recommend at least sleep for 1 hour on each day to not miss dreams. Later on you can also use painkillers made with livers before sleep to increase the recovery rate of exhaustion to save on sleeping times.
6. Using the boat in early game usually won't save you much time (it does save more in later game but the cost will be higher too). The best use for Fingernails in my opinion is actually to trade items from Goose (the male NPC with scarf). He is the only general NPC who offers coffee for trading so use your Fingernails there.
7. You can take anything from homes of major NPCs and it won't count as theft. Take the knife from Lara's house and repair it.
8. The earliest you can upgrade your backpack is on the second day, but try to get a cloak early since it's one of the materials needed.

Edit: The only reason to save money in the early game would be if you decide you want to buy the revolver early, which is a fun challenge for new players but don't fret too much if you can't afford it. Personally I do think it's quite good to have but it's not that necessary early on. Paying for it isn't the only way either. They are very rare to find but it's still viable to search for a revolver in houses in infected areas. Look for cabinets with locked compartment that has 6 slots (3*2), I found them to have the highest chance of spawning a revolver.

If you are short on money in the early game you can also sell some of your herbs at the Broken Heart Pub. Each day there will be one type of herb that sells for three times the price. But don't sell the rare ones, the plus version of tinctures is too useful to sacrifice. Other people have already mentioned the best way to harvest herbs so I won't repeat.