Nah, the original Enemy Unknown / UFO Defence didn't have any of that. It was just added to the new X-COM to streamline the gameplay, much like satellites and fixed loadouts.
In the original you had a bunch of countries that financed the X-COM project and at the end of each month you received money which you could use freely to buy new equipment, personel or base buildings (and ofc pay for the upkeep cost for existing stuff). So you could hire soldiers, scientists and technicians whenever you wanted, the only limited was the quarter capacity of your base.
Your monthly performance influenced your budged. Each successful anti-alien action improved your relations with the countries affected and some also had a global impacton all nations. Of course it also worked the other way around for failures. If your score with a nation dropped to low the aliens would send an UFO to negotiate - which caused the nation to resign from the X-COM project entirely. If your global score dropped too low, the X-COM project was cancelled completely and the game was over. Combat in the new X-COM just pales in comparison to that 10 year old game.
The cool thing in the original game was that UFOs spawned randomly and could be intercepted before completing their mission by either shooting them down or by sending a Skyranger with ground troops while they are landed. Of course you had to notice them in the first place, either via RADAR or by using airborne scouts (the latter was terrible inefficient, but I once managed to shoot down an alien base builder my Avenger stumbled upon while flying home). So the types of missions you had to deal with depended on the performance of your RADAR and interceptors.
Suffering a terror attack on a major city in the early game was horrifying - not only did you have to fight hordes of aliens with sub-par equipment, but you also had to save civilians - and the aliens often brought some extra nasty baddies for them. But you could have avoided that attack if you had shot down their UFO in the first place...
...in short: Don't bother with the new X-COM and get the old one from GOG instead. Not only is it more complex (and complicated), but it also offers a lot more freedom and randomness, which means each playthrough can turn out different. If you only want good tactical combat get Silent Storm. That game has amazing combat mechanics, an almost fully destructible environment and a decent physics engine.
Disagree totally here. The original, although a great game in its own right, had a number of significant negatives. Less is better in the new Xcom. It was incredibly tiresome in the original equipping your 16 soldiers before every mission with different gear. In the new Xcom, you have 6 soldiers max, so its much more manageable. You also get more attached to your soldeirs. This process is diluted significantly with more soldiers.
There was a lot more micro in the original. If you wanted to be successful, you had to work out the economy of building certain items, then constantly build them in your workshops, and then sell them afterwards. If your idea of fun is comparing the price of x with the market value being Y, then by all means. Personally i think this was a good design choice.
The combat is much better in the new xcom. It introduces a system of cover that wasnt really present in the old one (which relied on line of sight). It also avoids that horrible occassion when you have cleared everything and spend endlessly trying to find that one alien who has awoken after inhaling too much smoke. It is also a blessing that they removed time units. It was never any fun working out whether you had enough moves to make it to a certain point.
Also your part about being able to stop certain things from happening is only really true of terror missions and base attack. On alien infiltration (where the aliens try to sign a pact with certain countries), when they went for it, they often managed to get it. You would have at least 3 very large UFOs land in the target, and it was unlikely you would get all of them.
All that said, Xcom doesnt quite hit the mark in a number of areas. IMO these are:
No real base defence
Missions are not integrated well enough
Lack of strategy in base management
Lack of interceptor strategy (this was a fault of the original as well)
Game balance (its not bad, but its no perfect. Its very difficult at the beginning, then easy, then hard, then easy, then very easy)