My Lv.20 Bladesinging Wizard can prepare up to 25 spells. how many of each spell level 1-9 should I prepare?

Whatever works for you. But consider that you are limited by how many times you can cast a spell of certain levels. For instance, you can cast a 9th level spell only once, so preparing several 9th level spells is not gonna benefit you. I would really only recommend no more than 2 9th level prepped and ideally only 1. If you suspect you may be fighting a lot of enemies in large open areas then prep Meteor Swarm, but for days where you are very unsure a nice Foresight or Wish should be enough. 

Your preps should be about what you think you will need, and to avoid prepping spells of high level that you suspect you'll end up not having the slots for casting due to using those slots for other ones. 

If you're travelling then utility and defense may be better. A lot of fighting then more offense is better. But it's worth always keeping a mix because you never know. 

Personally I prep at each level the same number as slots for that level I have and then add the rest on the lower end with only a few extra maybes at higher. It keeps a nice mix without having the "well, I can't cast x because i've cast y" scenario be an issue. 

And always good to make use of upscalable offense spells to avoid having to use up preps for high level offense spells. Sometimes a couple castings of Scorching Ray will often serve better than using up your 3rds for a fireball. This frees up preps for more 3rd level utilities. 

Thank you for the advice. Do you also apply that same logic with other spellcaster classes?

Quote from Dawnrex15 >>

Thank you for the advice. Do you also apply that same logic with other spellcaster classes?

 
If they're prep-ones like druid or cleric, yes. 

Ok, thank you again :3

It really depends on the character and the campaign, the party, etc. There is no right answer. A few notes, which are general to all casters except where I've explicitly noted as being relevant to Wizards only:

1. You can cast a L1 spell with a L9 slot, but you can't cast a L9 spell with a L1 slot. As such, you need to ensure that you have a few lower level spells to take advantage of those lower level slots.
2. On a related note, you have many more opportunities to cast lower spells, so it makes sense to have your variety in lower spells.
3. Conversely, a spell cast at it's native spell level will generally be more powerful than a natively lower level spell being upcast to the same level. If you have a L6 slot and a choice between using it to cast a L6 spell or a L2 spell that has a similar effect (but varies in magnitude), you're generally better off casting the L6 spell. There are exceptions like Fireball, but you want some higher level spells to preserve the power of those higher level slots.
4. The result of 2 & 3 is that it should look kind of like a pyramid - having a lot of level 1 spells with a gradually decreasing number of spells for each level as you get higher. It's a rule of thumb, not a hard and fast law. It won't look like an actual pyramid, but it's a good way of thinking about the principle. If you have an inverse pyramid, you've done something wrong.
5. I'd disagree with CM and suggest you have multiple L9 spells. Not all of them, but you want a choice. At L20, you're going to be facing off against some major adversaries, so you want to be able to utilise.the full power of a L9 slot as needed. Personally, I'd say you'd want Wish prepared. If someone dies or you have some emergency prepared, you're going to want Wish prepared to get them back on their feet without a fuss, or a thousand other contingencies where you just want a spell to work. You also want another L9 spell that will allow the full force of the L9 slot to be utilised. Which depends on the circumstances. For example, if you're going to be fighting a vast army? You want Meteor Swarm, no doubt. It can do vast amounts of damage to the hordes of Mordor. If you're fighting a Tarrasque though, that's a waste. So think about it. Don't go above three though, it's pointless, because CM is right that you can only cast it once. I'd be very reluctant to have more than two.
6. Wizards get to cast ritual spells without having prepared (so long as they're cast as a ritual and they're in your spellbook, which you have access to). So, I'd never prepare those, but have them in my spellbook so I have a wider range of spells available to me.
7. Remember spell components. Specifically, note what spell components with value or that are consumed you have, because you have to have them to cast a spell that requires a component that has a value assigned to them or consumes them. For example, if you won't have access to a jacinth worth 1,000gp and an ornately carved silver bar worth 100gp, there's no point preparing Astral Projection anyway. You could use Wish, but you wouldn't need Astral Projection prepared in that case anyway, so it's just a waste.
8. If you get magic items, consider getting a [Tooltip Not Found]. It will allow you to store low level spells, which means you could free up prepares spells for other spells. There are other magic items that could do something similar, but there are too many to list, so I just wanted to get the concept across - peruse the list and see if you find one that you like.
9. Look at what your party is packing. If the Druid has Faerie Fire, then you can choose another spell instead. Or vice versa.

All those points will affect your spell distribution. Hopefully, they'll help you to understand the thought process, since there is no one right answer to your question. Generally, you want more lower spells than higher, but it really depends on how you're fitting into the party and what you're up against.