I'll answer this from a winded and somewhat scientific side of things, as the current other answers sort of hint at the variables involved, but of course there's no reason to limit yourself that way. I remember reading some strange piece of writing on a test that mentioned "verisimilitude," the appearance of truth, as a limiting factor in fiction - it should really be your ability to imagine. Magic forests grow powerful because of the magic and beings there, perhaps there's a mountain people who call on their God to keep the mountains safe - whatever the case, you should not let the physical world and world building come too much into conflict, that you have to redraft your previous world because it wasn't real enough.
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I'm trying to get the climates/biomes of some of the lands I've envisioned to work out as best as they can with the rules of wind/ocean currents and latitude.
You also say at the end that you want to determine the latitudes properly before the rest, but then again these are all related. The biomes on the face of the earth are a result of winds and oceans in the real world.
So let's put Earth up first, here's the ocean currents on earth (they vary depending on source):
And the prevailing wind currents:
And here's a visually busy combined map from someone (the ocean currents are likely more reliable here, and they are different. I'm not entirely sure how they turn on earth):
https://www.oceanblueproject.org/uploads/1/9/0/3/19034485/world-circulation-map-of-currents_1_orig.jpg
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* Latitudes are not the full story, and are often misleading. There is a large warm ocean current that flows from the east US and eventually to Britain. Britain is not too cold, but is at the same latitude as the lower parts of Siberia, which are very cold (an understatement, but this one's way higher in latitude). Minnesota is at the same latitude as Spain, north to south, but I wouldn't compare them in temperature, either. Hawaii and Egypt are at the same latitude, but Egypt's average summer temperatures are 15 degrees hotter in Celsius, and it is significantly drier. These three examples are the difference between being next to a warm ocean current, and being locked in (more or less) by land all around.
* While the wind at any given time can go in many directions, the prevailing winds tend to go in bands between the equator and the 30 and 60 degree latitudes (which I suppose you know of, since you think that is important to consider). 591
At those latitudes, there is often no wind, a historical complication for sea travel. The wind directions have to do with the rotation of the earth and something else to reverse the winds in the middle, perhaps pressure differences and the Coriolis effect but can't quite remember. Areas where the wind tends to blow from the sea and not over mountains will be wet - where it blows from the continents, it will be dry.
* When winds or ocean currents are allowed to go around the globe circularly with minimal land obstruction, they can form formidable patterns that change the weather in those areas. This happens on the Earth near Antarctica, where the "Roaring 40s / 50s" have both unobstructed wind and ocean currents. This would happen at the very top and bottom of your world without any polar regions, such as in the badlands or the islands down south.
These things are all a standard model, but there are exceptions, and specific large changes can occur also. Consider el niño, which greatly changes the global weather because one patch of surface water in the pacific heats up! This changes how hurricanes form, which has a special effect on climate some years' climate. I think that sort of thing (it's the year of the seven-year storm, etc.) could be a great story point, if that's your end goal with the world building. Also, there are local events, like Chinook winds in Canada, that completely change the climate locally for short periods of time.
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Humidity versus temperature are the main two factors you should consider. Ocean currents should be manipulated more or less as you see fit, and that would help make some areas more humid and affect temperature. But a savanna on a peninsula or plains/steppes that aren't continental are unlikely. Your biomes tend to be drier, especially on the western side (hemisphere?), but none of your biomes are really land-central enough to encourage that, so you would have to use some hand waving for yourself with winds to see how you could get dry climates by other means, like rain shadow. 591