Ever since I've reached puberty, I've had 3 problems with my underarms.
1. Hair
2. Skin darkening
3. BO
There are many ways to get rid of the first problem and they all come with pro's and cons. Also note that they also all have risks of ingrowns, etc.
1. shaving
+quick
+painless
+can be done continuously (you can always look "hairless")
+cheap on the short term
-expensive in the long term (considering how many blades you'll need over your lifetime along with shaving cream)
-hair grows quickly after one day
-possibility of nicking skin
-may cause skin darkening
I avoid shaving unless I'm in need of a quick fix. I think it's a good idea to have a razor stocked at home in case of emergencies.
2. plucking
+slow return of hair
+may be done at any time (you can always be "hairless")
+cheap (all you need are tweezers)
-time consuming
-painful
-may cause skin darkening
This is only to get rid of any stray hairs: I don't use it as my primary hair removal method.
3. epilating
+slow return of hair
+quick
+cheap in the long term
-painful
-expensive in the short term
-hair has to be a certain length
I like using this, except it doesn't get all the hair sometimes (hair grows in different directions) so you have to change angles.
4. depilating
+hair grows back quickly compared to 3 and 5 (not as quick as shaving)
+painless
-expensive
-possibility of chemical injury
-slow
Not something I'd recommend for underarms (sensitive as they are).
5. waxing
+can be cheap (DIY)
+slow return of hair
-hair has to be a certain length
-painful
-can be expensive (done in a salon)
When using hot wax, i tend to burn myself (darkening my skin in the process), and I can' get the hang of using sugaring or cold wax. I prefer having it done professionally, and be hairless for a around 10 days, but it does get expensive.