If it's possible to slightly exceed the small budget, this combination is not bad. For the blade, use the Donic Persson Powerplay. As a beginner, I think using an all-wood blade is the best option. For the rubber, you can use the Tibhar Quantum X, which I just saw on sale. I suggest using 2.1mm...
Xiom Vega Tour, Victas V > 11 Extra, Victas VJ > 07 Stiff, Nittaku Fastarc C-1, Nittaku Fastarc, BlueGrip S2, d09c, Rakza 9, and Andro Rasanter R45 are rubbers that I personally prefer to use for my backhand, in no particular order.