Which lens and magnification is best to see planets?
I just bought a Celestron Travel Scope 70 and it comes with a 20mm and a 10mm eyepiece. I get a good view of the Moon but I am not able to see Jupiter, Saturn or Mars as expected. I read about the Barlow lens but I am not sure how much magnification is required to view these planets. So based on my telescope, which lens should I go for? And should I also get Red/Blue filters to view them?
You should certainly be able to see Jupiter, Saturn, and Mars through your telescope. How is it not what you expected?
Perhaps some useful suggestions are here: http://astronomy.stackexchange.com/questions/8788/how-much-magnification-is-needed-to-see-planets-of-solar-system/8797#8797
The highest useful magnification of the Celestron Travel Scope 70 is about 165x. However, you are unlikely to find that much magnification to be usable except under very ideal conditions ("good seeing" i.e. clear atmospheric conditions, dark skies with no light pollution, viewing on a night with a new moon, etc). Even then the image at the eyepiece is going to be dim at that magnification.
Any telescope can in theory achieve an unlimited magnification. But in practice, its magnifying power is limited by the amount of light the telescope is taking in, which is to say, its aperture. The telescope is only collecting so much light. Every increase in magnification is zooming in on a smaller and smaller area, which means it is looking at a smaller and smaller fraction of the original amount of light.
On your telescope, the aperture is 70mm. This is the main thing that dictates how bright of an object you can hope to see at the eyepiece. There is another stat that is important to figuring out what eyepieces are likely to show you, though, and that is the telescope's focal length. Your scope has a 400mm focal length. Total magnification is the focal length of the telescope divided by the focal length of the eyepiece.
Your telescope came with two eyepieces:
400mm (telescope focal length) / 20mm (eyepiece focal length) = 20x magnification
400mm (telescope focal length) / 10mm (eyepiece focal length) = 40x magnification
As you can see, the smaller the eyepiece focal length, the greater the final magnification. If you tried an 8mm eyepiece, you'd get a 50x magnification. To get a 65x magnification, you'd need somewhere around a 6.2mm eyepiece.
(Interesting aside: Since the magnification also depends on the telescope's focal length, note that each eyepiece will have a different magnification depending on the telescope it is in.)
Before you go buying any extra eyepieces, though, I'd strongly recommend you go see what you can see with the equipment you already have! You should certainly be able to see Jupiter, Saturn, and Mars.
Jupiter will appear as a disc. You can see its four Galilean moons, Io, Europa, Ganymede, and Callisto, so-named after the first person to see them, Galileo. They appear as points of light around the disc of Jupiter.
For Saturn, you should be able to make out the rings poking out either side of Saturn's disc. They look like tiny little teacup handles. You can also see Saturn's largest moon, Titan.
Mars is a little bit less exciting, but it should be visible as a reddish disc.
If you do opt to buy another eyepiece, one thing to pay attention to is eye relief. Eye relief is how far away from the eyepiece you can be to still see a decent image. Eyepieces with shorter eye relief are cheaper, but they are also harder to use. An eye relief around 6mm to 8mm is much more comfortable for me.
As for me, I can never help myself: for every telescope I've owned, I always buy an eyepiece that pushes the limits of my telescope, just to see what it looks like. But from experience, I can tell you it is not a great view. Still, it can be fun to see what your equipment can do. But before you jump all the way to an eyepiece that gives you 130x magnification (or whatever), I'd say to shoot solidly for the middle range of your scope (in your case, maybe 60x - 80x). If you can afford it, buy a mid range eyepiece with decent eye relief and field of view (FOV). You'll be much happier with the view through this eyepiece than you will an eyepiece that maxes out the magnification.
Do yourself a favor and at least pick up a lunar filter. They filter a certain percentage of the light and allow the rest through without modifying the color. The moon is so bright, it will make your eyes water trying to look at it through even a modest telescope. Lunar filters make looking at the moon a much more enjoyable experience.