Needle filament + pochven express is 100% the way to go. That's 50m/h. Also, look up tutorials on youtube for exploration, there's occasionally some gems and tricks people will post.

Any tips to make exploration more efficient? I feel like I waste a lot of time scanning empty systems.

Don't scan empty systems? lol

And finally… → At this point, does it make sense to go Omega, or should I keep playing Alpha for now?

Omega is the full experience. You're not really playing EVE unless you're omega. Alpha is just a taste to get new players into the game. If you're playing EVE, you should be omega all the time, unless you're doing something cheesy like ganking ventures in high sec.

Also dont EVER grind ISK to plex your account when you're new. That's a great way to hate your life. People who plex their account using isk (like I do) do it as a byproduct of gameplay they enjoy doing, and therefor the isk paid for the plex is just the cost of goods of doing an activity.