First of all before you jump, do exercises to ensure that your hands can be stretched out enough. You can do so by taking your finger no. 1,2,3,4 (4 is the pinky) and place it on the 5,6,7,8 frets on the low E string (topmost/thickest string). Play each fret with each corresponding finger while picking up and down alternately. This will ensure that you remain in flow and your right hand does not get stressed. Start out slow, no need to rush. Also, ensure that all notes sound clear and not dull. If it sounds dull, just press down harder (this might hurt your fingers, but you will have to endure it for now. Take breaks between sessions). Once you've gotten a hang of that, try the same on the next string and so forth till your fingers get free. I know that it is not the most enjoyable thing to do and that it takes a lot of time to master, but trust me that it will help you in the long run. Remember that there are no shortcuts.
As for tuning, I guess you are using daTuner to tune. Ensure that the tuning is in this sequence for the corresponding strings from top to bottom : E2 A3 D3 G3 B3 E4. Its ok to break strings once in a while while tuning, just remember to keep a spare set handy.