OK for the above ^^^^, but the 'standard' string gauge is really those that were on it from new (typically 10-46...) Most brands are OK (I use Elixir...
... which cost a little more, but last a very long time, and play and sound good, to me; other brands are good, too...). If you're bending strings unintentionally, you're gripping too hard the neck. Is the guitar supported properly (not needing your left arm to hold the neck up...)..? If not, get a decent strap, adjusted so that the guitar stays in place 'arms off'. There's never any need to use much pressure on the strings, for solo work nor for chords. When pressing down on the fingerboard, try, as an exercise, to use only as much force as is needed to get the strings to sound out clearly, no more. Make each chord shape, and make a conscious point of using as little force as possible. Do this, as an exercise, before each session, and see if it helps. Are your fingers being applied directly downwards, and not at an angle, pushing the string 'sharp'..? Again, take care when playing to think and look at each finger, slowly, to make sure it's all good.
Of course, a lesson or two with a competent tutor should sort out issues like this, so I'd recommend that course, if at all possible, just to get this technique issue sorted. Ye, heavier strings will be harder to push out of tune, but it won't correct errors being made, which will remain for decades to come if not jumped on early (No, I don't mean to suggest that you jump on your fingers; that would be silly, and would hurt ...). Hope this helps.