$300/month for a 24/7 gym that includes combat sports training from actual former pro fighters is just a few hairs above that of a steal in your favor... if you wanna actually learn to box with the intent of going pro.
I'm gonna say this from the perspective of someone who, to powerlevel a little, has engaged in combat sports extensively since 15 years old and continued pursuing until 28 years old. You need to consider what value you're going to get out of it in relation to the value you're putting in - to me, if I were still fighting, I'd be getting a lot out of that since it'd be a reliable location to train among peers and improve my skills.
If you're a regular joe, you're paying a more sizeable amount for something that may not see much long-term use but will keep you physically fit. If money's no object and you like that level of fitness and to learn a way to defend yourself that's likely tested, then there's no real argument against it.
That being said, do your research on the gym. Learn what fighters have come from there, learn their records - including the guy you talked to, look up the actual coaches, look at their records and the records of their trainees outside of the gym. You're not looking for a bunch of 30-0 martial gods, you're looking for guys who clearly have a good amount of fights under their belt - even a record of like, 3-3 is more substantial than a guy with a record of 3-0 since they're going to have more experience fighting under the constraints they'd be training you under. You also wanna make sure those records are either recent (for the ones still of fighting age) or within the appropriate bracket for their fighting age and they're still in respectable shape.
If they've got boxing training, they likely have pro boxers, see how many of the fighters they take credit for still have active boxing licenses (If your country requires them). Guys who get into pro boxing and quit tend to have inactive licenses since they're not gonna renew them.
When you go in for the lesson, take a look around the gym when you have time, look at the equipment, see how new or well-maintained any of it is. If it's all shiny and brand new with not a lot of people using it, it means they spent a lot on new gear for not a lot of patrons. If it's good quality but clearly under frequent use, that means there's clearly a retention rate.
Oh also, check the ears - you said you like combat sports, you know what cauliflower ear looks like. Also if they've got small chests and big shoulders, they're definitely keeping themselves in fighting shape, which is always a good marker, though a good coach isn't always gonna be in fighting shape - Cus D'Amato's best years as a coach were when he was a tubby little midget.
And also remember, of course, this is a privately-owned gym, they need money to keep the lights on and to eat. They're gonna want that money out of your pocket, even if they've got good intentions. Remember that whatever they do, it's going to be with the intention of getting a transaction out of you, even if they're ultimately interested in helping or befriending you.
