There's a little ambiguity about if you can retain your Staff Nexus features when you pick up a new staff or not. You can certainly craft starter staff into another staff, so say your DM let's you transfer your Staff Nexus features into the staff you found or you use Craft to upgrade your original staff into an Animal Staff:
When you make your daily preparations the Animal Staff will automatically gain charges equal to this highest level spell you can cast. If you're still level 1 it would be a little weird for you to have a Level 4 item Animal Staff but you would get 1 free charge just from the staff. When you reach level 3 on your Wizard and unlock level 2 spells the number of free charges you prepare into the staff will increase to 2.
At the time of preparation you may also expend one of you spell slots to gain additional charges in the staff equal to the slot level. If you're a level 1 Wizard you have only 1st level slots to expend and that will be 1 charge.
At first level if you expend one of your spell slots your staff now contains:
Cantrip: Ray of Frost, Know Direction
1st level: Summon Animal, Magic Fang, Magic Missile
Charges: 2
You can use these charges to cast any of the spells in your staff that exist on your spell list. Magic Fang isn't Arcane but you can spend your two charges to cast Magic Missile twice, Summon Animal twice or to cast one of each of these spells.
When you reach level 3 on your Wizard you'll automatically get 2 charges in the staff with your daily preparation for free (free charges grow with your spell slots). You may then choose to expend a 1st level slot for one additional charge or a 2nd level slot for two additional charges. This means on any given day you might have anywhere from 2 to 4 charges, which can be spent casting any of the staff's spells in a spontaneous-like manner.
The value of Staff Nexus in this case is that it allows you to put one extra 1st level spell into any staff you find (though rules still require some clarification). You should note that the first level spell you choose does not heighten as you level. For this reason it may be advisable to choose a spell that retains its utility throughout your character's growth. At level 11 the ability to cast 1st level Magic Missile spells with your staff charges may not be very useful. The ability to cast Fear or True Strike many times per day may be better for you.
