Hello :-)
> Can you recommend some barlow lenses?
The TL;DR: None. :-).
What eyepieces do you have?
If you only have the kit eyepieces: For the price of a good barlow, you can get at least two decent eyepieces.
Conbining the kit 10mm eyepiece with a barlow is just not great.
> best magnification
The atmosphere will limit magnification. Even 200x is a stretch if the planets are low to the horizon & the conditions are not great.
If conditions allow, 300x can be nice... But doesn't work often. A 4mm 58° type is often on sale (not a cheaper short eyepiece due to poor eye-relief).
Else the 6mm 66° (or the 58°) are the way to go. Often for $30-$50, sometimes $20-$30. Depending where you're from and where you're buying.
Where are you from?
6mm 66° <$38 (The 58° is actually better, the smaller afov aside)
4mm €27 (Atmospheric seeing conditions will not let you use this very often. But if it works, it's nice. The field of view is small, the planet will transit quickly. Short good wide-angle eyepieces, e.g. 82°, cost quite a bit. This is where a barlow can make sense: Getting a $100-$200 6.7mm 82° for example, and then using a good barlow for when the seeing is excellent! :-) )
Clear skies!
I spend way too much time on here and making all sort of doodle graphics :-)
Also let me know if you want some better planetary eyepieces. Some are currently on sale on Amazon for insane prices, for whatever reason.
Older Info-graphic on the 114/900- eyepieces, field of view, magnification
Under €30 atm,
6mm for €24 while in stock, https://www.amazon.de/Akozon-Planetarisches-Okular-Planetenokular-Astronomie-Teleskop-Monokular-default/dp/B08SPX3H94/ (usually €40-€50).
5mm for a bit more https://www.amazon.de/Mugast-Planetarisches-Weitwinkelokular-58-Grad-HD-Planetarisches-astronomischen-default/dp/B083W412TJ
(The 6mm 66° is sometimes even cheaper, not at the moment though. Never mind it's also on sale. A bit wider apparent field of view, otherwise the 58° have better viewing properties. Still a very nice budget eyepiece)
Good luck, have fun!