Note on opening the ruins before the war: I mention this a lot, one of the future investments will be worse if you don't open the givini ruins before the erosian war, so if you're going for a high score of returns in a single investment round, you need to open the ruins before the war. In terms of total ProN earned in a playthrough it's almost certainly worse hough. The ruins being open early does let you completely shut down a force of evil in the world from influencing the erosian war though.
The reason to skip Yhilin bank is because it is less profitable than the other two banks, not because you can buy it earlier chapter 4. You can't really afford it early in chapter 4 if you want to open the ruins before the war. Also the hidden scores for buying the yhilin bank are only added if you buy it before the battle of yhilin. You don't need sanitation mages if you're not opening the ruins before the war so you can afford to buy all 3 banks AND premium steel if you're going that route.
Anyway, you must buy the Ivalan bank investment, invest at least 50k into the order of silence(You can spend 200k on it later instead if you don't buy it now, but you'll miss out on a massive RP boost after the summit if you don't invest now, and 10k is too little), 10k invested into arigarda, 5k invested into iron cudgel, 10k in bribes to ace the votes in the summit. 100k invested into joining the merchant guild is good too.
400k for the Ardan bank is an amazing deal and your ProN returns will cry if you don't take it. You need to buy a few other investments to get it that low in price though. Going all the way for 300k Price probably isn't worth it as already said though. It's not actually needed for anything despite that though.
the 10k investment in the incubus king cache permanently boosts Simon's stats a little bit and you'll never be able to buy it again if you don't. I consider that more valuable than ProN but it's skippable if you don't care about it.
If you buy both the 5k public works AND the 5k bridge you get enough Janine RP from that that if you got every free Janine RP boost you can get her RP high enough for her to earn you an extra point of Ginasta RP later which is hard to come by. I would use discretionary funds for the bridge instead if you aren't buying the public works though.
The 10k investment for the dusty horde isn't needed at all imo, but you will probably lose 40-50% of your discretionary funding and some rp from chaos and lower VP if you don't get it. You have discretionary funding to spare though if you researched orc diversification instead of essence shielding, and the chaos might make megail 100 impossible after battle of yhilin if you were aiming for that. So you probably need this to get megail 100 there.
Ardford Supplier or mercenary flotilla will add 5 to your final army size after the third arclent war. You ideally want that value to be 175 or higher, but it doesn't matter that much. Mercenary flotilla also adds some Ardan score but it's almost certainly not worth it.
Deeds of Vinario is almost completely worthless but it does do 2 things which are quite good. It adds 5 Megail RP, and 5 Trin RP. If that's enough to get an extra Trin Max Copy or have Megail 100 after the battle of yhilin ends it can be worth it. It's worth some arclent acceptance and takkan score later too, but those scores are both excessive so far if you do everything else right.
Premium Steel needs to be purchased round 2 of chapter 4 at the latest in order to get all of the Unique gear for your party members, but if you don't buy it before the third arclent war, the profit it gives is terrible. If you do buy it before the third arclent war, it makes tons of money selling weapons in preperation for that war and completely pays for itself and than earns you 10k in profits every round after that. It's very profitable to buy now. It also adds some Aka RP which can help with the battle of yhilin, and it's kind of nice for Robin to have her crystal before the third arclent war. If you don't need the 2 aka RP for the battle of yhilin, this investment can actually be bought during chapter 3. This can be useful if you're buying the yhilin bank now since buying both bank and premium steel can drop your ProN below the 1million needed to qualify to join the merchant guild. You can still join the guild after the unmen investigation is completed if you need the aka rp though, that just means you'll have 1 less point of investigation. Being 1 point short on investigation still maxes your vhala RP though, and you have Dari RP to spare so if you have essence shielding researched I wouldn't care about not having merchant guild membership until after you get the bribe for voting how the merchant guild wants you to.
Buying the Sanitation mages now is pretty much a necessity if you want to open the givini ruins before the erosian war and have a perfect council of gawnfall and Return to Stineford. If you aren't going to open the ruins before the war you can skip it since the givini tunnels investment is enough for a perfect council of gawnfall without it, you just can't afford that before the Council if you're buying the Succubus Tower Expansion and opening the ruins before the war. Buying it now also earns Tina some support in the Ardan succession but we have no idea how important that will be yet. It does give ardan score for lowering the price of the bank though.
Ardford Restaurant is way way more profitable if you buy it now instead of later, and Crystal refinery is rather profitable if you buy it now too. Both give ardan score and can be used to help lower the price of the bank to 400k. Neither one is really critical for anything to be bought now though, but you'll want the restaurant eventually to help out a mother and her adorable daughter.
The expatriot program is pretty much worthless, especially if you got the ardan embassy, but it does give some scores and can't be bought later.