Own a 700d.
Similar position, liked photography and did what I could with my compact Ixus but wanted to get a DSLR.
When I was looking my choice was the 600/650d or grab the newly released 700d. They were roughly equivalent and all the reviews said if you're upgrading from the 500 to 700d then it kind of made sense, 600/650d then not enough difference to justify the premium. If you are coming in fresh, take your choice based on what price you could find. I'd say the same applies here, if you have the cash get the latest /greatest and bear in mind that it'll be old news within a year. Or save some cash and get a 700d or a 600d and spend the rest on lenses.
So I planned to get a 600d or 650d as the prices had dropped since 700d released and I was planning to save a little cash. But then I found a deal on body-only that meant I could add the newer 18-55 IS STM kit and 1.8 50mm for the same sort of money as some of the bundled 700d's and 650d's I'd seen.
So (1) 750d has some nice upgrades vs the 700 but both will be great starter cameras. Buy based on budget and availability. Neither is a poor choice, probably more versatile bundles and prices on the older model.
(2) the kit lens is fine for family shots and travel pictures. You'll probably want to expand that range and quality once you've done a bit of photography and get an idea of what you like to shoot most. I bought the 50mm 1.8 nifty fifty immediately and found that whilst the added zoom effect of 1.6 crop (making it equivalent field of view to ~78mm) meant it wasn't always ideal for smaller indoor environments but took some lovely portrait shots. Then I dropped the 50mm after about 4 months and the focus in one corner got a bit fudgy. So basically lived with the kit lens for the first year.
It had limitations but I still took some great shots and learned what i wanted to get. So once I had a bit of cash I upgraded to the Canon 50mm 1.4, bought the 24mm STM pancake for mid distance landscape and walk around. This week I've just bought and then immediately returned the Canon 70-300mm IS (because it was disappointingly soft past 200mm and very patchy AF). I then ordered a 2nd hand Sigma 70-200mm 2.8. I plan to get a proper wide angle and may upgrade my 70-200 to the Canon L versions if I find myself using that a lot.
So that'd be the other advice, whilst the kit lens will be ok you'll find certain shots you like to take and that will need more specialised lenses. Whilst you probably want to budget twice the cost of the body camera in extra glass don't go banzai in the first week. Wait and see what you use it for most and invest in something in that range.
(3) I faced the same choice and heard much the same. Chose Canon for usability, some of their 'famous' lenses and reputed better video. Been happy enough but no Nikon to compare against for ultimate IQ. Some of the shots with the 700d on kit lens have come out beautifully, performance with the 50mm 1.4 is as crisp as I need. There may be a difference at the very highest quality levels for Nikon but the shots I've taken have been plenty sharp enough for family shots and hobby stuff.