Basically you have Cremant type sparking wines which are produced from other regions of France besides Champagne. It is just like Champagne just that other French regions like Loire, Alsace, Bordeux etc are not allowed to call it Champagne.

So just like Armanac's are like Cognac's for lower price, good Cremant will be cheaper and more enjoyable that cheaper Champagne (I've not had any really expensive Champagne).

Then you have Cava from Spain which is similar process to Cremants and Champagne. The difference would be in type of grapes used. A friend of mine swears by Cavas just like I swear by Cremants from Loire region. However my wife hates Cava.

Then Proseccos from Italy again are similar, but quality varies more.

After that we get into more questionable cheaper sparkling wines which usually means some sort of out of bottle insertion of CO2 and even worse version include some other modifications such as sugar.

In general to avoid literal headaches you want BRUTs. Anything semi-sweet or sweet is suspicous.

Again I am not a full wine expert but this is mostly years of ahem experience.