A good question for most. You must have enough available for the draft, Internationals, player advancement and possibly getting some spare players due to injury or fatigue problems. An experienced owner can get away with $1M to $1.5M or less rather easily. $2M to $5M pad is good for the inexperienced because they don't know the pitfalls that may come their way.
For the Draft and Internationals, bonus money comes from the Prospect Payroll while their actual salary comes from Player Payroll, something to keep in mind.
If you go to the previous Draft history you can get an idea of how much Bonus money it will take to sign a first round pick. Normally, the first pick asks for $4M and it slowly drops from there. However, a selected player may have signing issues where they may need to be enticed with much more money. Some even refuse to sign.
Internationals is a little different as several teams may be bidding for his services and the price can get rather outrageous at times. However the Bonus money comes from the Prospect Payroll while his salary comes from Player Payroll.
There are many times where players get injured and is a big sore spot with owners most of the time. Having your best player go down with an injury can cause serious problems if your a frontrunner and don't have a qualified replacement in the minors. Money could be an issue if a trade is in order to solve the problem.
Players suffer from fatigue also and need to rest throughout the season. This happens in the minors as well as the majors. In the minors you can have extra players on the inactive roster to solve the problem. It is not uncommon to have 2 or 3 pitchers and a couple position players on that roster at each level. The reason you need to worry about fatigue is a player is more susceptible to injury as he tires. Pitchers especially need to be at 100% before they pitch as a tired pitching staff can give up lots of runs and recovery can be near impossible. The majors you just have to use what is available and the reason for viable backups for each position.
Another thing you might want to consider is picking up a player after the trade deadline, you might be surprised the number and type of players that hit the waiver wire when that occurs.