Some wonders you can legitimately try and get most of the time. Wonders like Hubble Space Telescope, Brandenburg Gate, Oracle, Porcelain Tower, Pyramids, and some of the Ideology specific wonders come to my mind. Stonehenge is tricky but highly possible, especially if you can get free Mining and/or with stolen workers chopping some forests. If you can get a GE, either from Liberty finisher or any other means, you can try and get other wonders (Macchu Pichu and Leaning Tower of Pisa comes to mind) but it will be close nevertheless. You need to get to those techs fast, and sometimes even if you do, because AI start with more techs than you they get there faster.
Wonders like Chichen Itza (extremely difficult), Parthenon(not a high priority one but still it's highly valued by AI), Great Library(pretty much impossible in Deity, on standard it is built between t.21-32 latest), Notre Dame(similar to GL, almost impossible) and Petra(this one's more doable, however even if AI has 1 desert tile available they will go for it) are very difficult to get in Deity without a GE (I suppose maybe with Spain and King Solomon's Mines one can get Great Library).
Wonders like Hanging Gardens,Uffizi,Forbidden Palace are almost always coveted by AI aswell and not that easy to grab without a GE. With a GE, you can get them most of the time. Same goes for most of the religious wonders. In short, I think if you get a GE and the tech/policy/ideology, go for it. If you have great production in your capital, go for it. I built 16 wonders with Venice once and only 1-2 were GE rushed. Some games it's possible, however don't let wonders make you miss the bigger picture (growth, science, culture and warfare, whatever you're intending to do). Their bonuses are welcome but outside cultural victory and maaaaybe science(Hubble and PT Helps immensely), wonders are not mandatory for a successful game.
In some games, it will be tough to do what you're planning. Such as my latest, playing France going for CV, Pedro was my neighbour who built Great Wall, and built a ridiculous amount of wonders. GW rules out early conquest, Pedro gets most wonders so wonders are ruled out as well, and also he is 8% (which is like 5 techs) ahead of me in tech, even though I'm focusing on science and growth like crazy and my NC timing was fine. Come to think of it, I think I should go Dynamite and try take him out, then focus on culture. Maybe I'll go back to that game, who knows.
I have beaten Deity multiple times across all victory conditions, however that doesn't mean I can win every game I start, I pretty much abandon half of my games. Keep going at it, and on your first tries, go for simple, like Science Victory with Korea/Maya/Poland or Babylon. In my opinion, if you can nail how to focus properly on growth and science well, the rest is only about refining how to channel that into various victory conditions.