So, I've been having a great deal of trouble going from normal mode to Classic mode. My main problem is that I have countries jumping ship too much and I can't get the money and the facilities built in time to stop them from doing that. I think my biggest problem in Classic mode is money. I'm starved for it with constantly trying to buy new satellites and arrays in the first two months. I know I should be focused on getting those satellites up in the first month or two, but I never have the money to effectively do that. Should I be selling off corpses left and right? Should I be taking only the abduction missions that net me money, or focus still on getting Engineers?
The Africa bonus helps later on, but in the beginning 30% of not much is not much. You absolutely have to get those satellites rolling. You also just need to deal with a little bit of luck, and hope that the nations starting to get bad panic are the same ones who pay well :)
Focus on the engineer missions first, you need to collect engis to make more uplinks/any workshops.
Remember that you can build satellites BEFORE having the capability of launching them, which helps ensure at least 4 birds in the air at the end of month 2.
In the beginning of the game, I sold power sources/flight modules/all my corpses pretty compulsively.
This is not specifically a money problem. You also need to 'manage' your panic levels. You can achieve this in a number of ways;
If a country is already at 5 panic - and all your other countries are at 1 panic, then you should consider NOT doing a mission on the 5 panic country, if you have a satellite to launch at the end of the month. See below.
You need to 'plan' your satellite and uplink construction. Generally you always need to be launching 2 satellites each month - and this is a pretty easy goal to achieve.
The most important tip is only EVER launch your satellite on the LAST day of the month. This way you can ensure you pick the country(s) on 5 panic, so they don't leave. If you have more countries panicking than satellites, then you focus on which ones you want to keep. Ideally let a country from your home base continent leave, because you already have that bonus. If you have less countries panicking than satellites, then work towards a continent bonus you want.
Finally - consider the money each country gives. United States gives $180 per month, while other countries only give $60.
Early on consider selling just about everything EXCEPT alloys, weapon fragments and elerium. Never every sell those (you'll regret it later).
I sell the first couple of UFO power supply and UFO navigation equipment (even the 'working' ones) - because the amount of money is huge, and often means and extra 1-2 satellites really early. I tend to find that by the time I'm ready to research and build items with them (such as Firestorm) - I have more than enough.
Taking into account the above points, it is generally best to get as many engineers early on as possible. You need engineers not only to get more up-links, but the more engineers you have the further the price of the satellites themselves goes down. i.e. You start with 5 engineers, and the cost of a satellite is $100 each. With 9 engineers (after the first mission) each satellite only costs $67.
Using this tactic - you should NOT start building satellites until there are only 21 days remaining for that month (i.e. build on the 8th for Feb, 10th for March etc). This means you maximize the chances you will have more engineers before building the satellite (which you will launch on the final day of the month) and thus have the cheapest satellite possible.
Finally - one little 'trick' - if you ignore the first "small" UFO it seems there is an extremely high chance (5 out of 6 for me) chance you get get a Medium UFO about 1 day later. The standard interceptors and missiles take this down easily, and you get A LOT more corpses, UFO parts and items. I got 4 satellites up in the first month on Ironman Classic using this approach.