I have heard that one have to use a basecoat of some sort. Some use spray, and other enamel, I think (or is it so?).

Which one is best for sherman tanks or tiger tanks? Can I use matt white spray for it?

If you mean "primer" for basecoat, I use an acrylic white general purpose primer that I buy for a reasonable price (1/3 of the price for a Tamiya primer can for 500 cc to be diluted roughly at 60% with plain water). I'm very happy with it mainly for four main reasons: I can airbrush it, It's odorless and atoxic, it primes exactly like Tamiya (on top of that I cannot get on with the spray cans, but this is my personal problem) and it's cheap.
You can see the results in the following post

https://armorama.kitmaker.net/forums/9091&page=1

Ciao

I've never done a base coat and was wondering what is the point of a base coat?

It's something you do to help identifying any problem or imperfection you've done during construction and to fix other minor problems like tiny scratches and so on. If on plastic cannot be 100% necessary I personally think that you have to use it on resin kits.
Ciao

Sorry guys, I didn't mean a primer.

If I paint a figure with red cloak, I paint a basecoat of red.

What can I use for a Tiger / Sherman or alike tank?

Well, If you are doing a camo pattern, use the lightest color first. i.e. Tiger would be Dunkelgelb then a dark green then dark brown. The lighter colors are more easily covered by the darker colors...especially if you spray. A Sherman would be an Olive drab, then washed/drybrushed. I think you will find that armor isn't that much different than figures.

When doing German armor, I prime the tank with black, then do a basecoat of Tamiya Dark Earth. I then apply Tamiya Dark Yellow mixed with some Buff. Already at this stage you will see a nice amount of shading on the vehicle. You can then can choose to lighten further or move on with weathering.

I haven't done an Allied vehicle, so I am not sure what base color I would use.

Stuke

Basecoating depends on the weathering approach you plan on taking. If you want to do pre-shading, a dark basecoat would be appropriate.....I would use black for this on a Sherman and maybe a dark brown for a King Tiger. If not preshading, I've never used primer coats on plastic models, just going straight for the lightest color in the camo scheme.