The best option for you is to get a Slingbox SOLO, the Network Bandwidth for Standard Definition streaming is 600 Kbps or higher, since you have 1Mbps for upload, it will work very good at the remote location. For Mobile Streaming, the bandwidth needs to be 150 Kbps or higher.
I mean will i be able to continue doing whatever i am doing normaly without having lag problems or even disconects due to the heavy transfer rate?
Yes, at the Slingbox location you will not have any issues with Internet or the transfer rate.
You can check the Slingbox SOLO requirements here