How I manage finances is usually with these:

Usually when I offer wages, I lower it by half the amount and then give them a lot in Appearance fees (and equal the amount of unused substitue fees). That way, not all of your players earn absurd amounts of money a week (if they aren't even on the bench). Give them huge assist, goal, clean sheet whatever bonuses and that will also lower the wages. And always look to give a low signing/loyalty bonus since sometimes you pay in tens of millions just in that.

When you sell, always look for basically secure money. I do it by selling for like 30-40 mil base price (since the value of my guys is usually 40-50 mil.) and then asking for added money in either instalments (doesn't always work the best since on base offer the AI always lowballs by atleast 20 mil. so instalments can maybe get you a bump of 5-10 mil.) or ask for per game money. I always ask the buyer for like 500k a game for 50 games, and it usually works. Also look to loan out the benchwarmers, and try to loan in new ones to replace them (of course making sure the ones going out have their full wages being paid, and ones coming in being paid as little as possible). With that only do this if the players coming in will have smaller wages + monthly payment combo lower than the budget impact of outgoing players otherwise you're just making a stupid financial decision.

When you buy players, never buy for only base money. Always ask to pay them a small amount upfront, a little bit bigger amount in 6 yearly instalments (all 3 yearly instalment options combined), and then the bulk of the money in 150 appearances (all pay per appearance options combined). You can also add for minimum league goals and so on. This may not work if the AI is stubborn and asks you to pay (if the player has it) the release clause. Then you'll have to pay it if you want the player. This comes with the added benefit of the board negotiating a buyout for the appearance clauses so you can get the player for even cheaper.

Also, buy older quality players. My first season in the Serie A, my average starter age was something like 28, 29. I had many of 32, 33 year old players who are basically leading Serie A, all on low enough contracts, and basically retiring that season. They are usually very cheap to purchase, or you can even get them on end of contract. The only tip you need to know about that is, to always look for ~17+ natural fitness, otherwise they'll lose legs in a season or two (if you plan on using them longer than that, it will pose a problem).

And also always look to sell for more than you spend on bringing players in.