The optimal number of bases you need to build is three. When placing a base, the three circles indicate your potential radar coverage based on the number of radar arrays you build, with the third outer circle representing your maximum possible range. Plan ahead so that you maximize land mass coverage while not redundantly overlapping with other bases. I built my first base in the Middle East, one in Central America, and one in South East Asia and was able to cover most of the world.
In the beginning, spend most of your money on aircraft. If one of your aircraft gets shot down, you won’t have to buy a new one to replace them but they will be out of commission while they are being recovered and repaired. UFOs will be coming at you hard and fast so it’s vital that you have enough planes to deal with them. Foxtrots will be viable against heavy craft for a surprisingly long time due to their dual torpedo load out while the starting Condor and its upgrade Corsair is necessary for smaller, agile fighter type UFOs. Of course, still phase out outdated aircraft when you can but more importantly build up a large air fleet as soon as possible.
If you are good at Micromanagement, the air combat minigame can be cheesed so that even encounters with a low autoresolve chance can still be won if manually controlled. Use pause liberally. Manually change the bearing of your planes so that they aren’t flying into enemies head-on. Use the hotkey to repeatedly dodge and circle strafe UFOs. Lower your thruster speed when behind them. When firing torpedoes, stagger your shots (i.e. fire one round after the other) so that the enemy is unable to dodge both. There’s a good video online that will explain air combat better.
You don’t need a squad at every base you build and one squad will be enough to handle your crash sites for the first few months. Some bases can simply be hanger/radar coverage bases from which you launch air sorties. There is a chance that the aliens will try to invade your bases but it won’t be a real concern if you are vigorous with your air superiority.
Build hangars and radar arrays at new bases first, otherwise they’ll be a pointless money sink. You can think of building other additional structures after that.
Multiple laboratories will increase research speed which is very beneficial. Research can help you get a leg up on aliens because they’ll unlock items such as aircraft weaponry and personal explosives that are immediately available and replace existing stock without having to be manufactured, plus it provides passive bonus against enemies through autopsies.
The first armor you unlock isn’t that effective for its cost of research and manufacturing price. I tend to skip it in favor of better weaponry and wait for better armor.
When looking at troop stats, place an emphasis on bravery because it is the one stat that’s hard to raise yet becomes crucial against later psionic enemies. While earning combat medals can raise bravery somewhat, it’s better to start with a high base bravery stat when recruiting.
Soldiers with high accuracy are naturally good with sniper rifles, high strength should be given machine guns, high turn units benefit with a shotgun or shield and shock baton, and reflex do well with the standard rifle or shotgun.
Scout areas and door bust UFOs with your shield and baton users. Have your high reflex rifleman save some TU at the end of their turn so that they can provide a sort of overwatch against any aliens that might pop up. Snipers should be at the back with a clear line of sight. Use machine gunners to break up cover and suppress enemies. Run up and flank with shotgun users for point blank instakills.
Crouching increases your own hit chance while reducing the chance of the enemy hitting you, so use it often. Targeting an enemy and right clicking spends TU for better accuracy. It’s better spend as much TU as possible for the best chance to hit rather than taking multiple potshots.
Try not to fight at night, it’s much more dangerous and frankly more tedious hunting enemies at this time. You can delay missions by having your transport ship circle the crash sight until day time.
Make use of all the assorted grenades. Toss a stun grenade into an enclosed space such as a crashed UFO, then back off and wait for aliens to pass out. Drop a smoke on your exposed squad members for extra cover and safety. Flashbangs are good openers to suppress enemies so that your shotgunners and riot shield guys can get in close. While explosive grenades destroy enemy loot and only trigger at the start of the enemy turn, they are great for that really dangerous enemy that’s coming around the corner.