I feel like these online issues were way more prevalent after the early access day expired, and everyone was allowed in. Gotta be some server overload of some sort.
Anyway my thoughts:
I only got to play on early access day due to... well you're all aware. At first I couldn't get in, so I did trial fights, just to learn the controls and get a sense of the gameplay.
Tutorial Mode is okay. I get the gist of the mechanics. I was hoping (maybe it will be in the full game?) it would be as in-depth as the Guilty Gear RV2 game.
No practice mode. Really going into online fights blind. So, no bueno.
Online fights. I did not have a boat load of trouble getting matches. Longest wait time was definitely under 5 mins. If the connection was good, I got decent matches. I had a hot streak starting out, but then the connection got crazy, and lost plenty fights due to the constant freezing frames. When I thought I blocked...I was not.

And towards the last of my play-time, anytime the rematch prompt appeared, the beta client crashed. It was weird.
Character selection. I like the roster they provided. I have not yet gotten to play with every character. Adult(?) Gohan is a serious problem. A little button mashing and potential unlock, can make any noob a nuisance. Also, I think Kidd Buu has an auto-combo that is almost unavoidable (assuming you're online with poor net code). It is a low kick (underground kick with long range) into his stretch kick/headbutt closing the distance, into another hit, leading into his Human Extinction. With a little lag not reading some block commands, a button masher using overwhelming offence at all times, and an infinite loop of that combo, Kidd Buu is definitely a force online. I played against someone who was mashing buttons the entire match, until it got down to Kid Buu. Used Sparking Blast then killed my whole team. Killed my Saiyan Spirit.
My go-to team was Vegeta (duh), Freeza and Cell. Second String Adult Gohan, Beerus, Cell.
Overall. If it wasn't for the server issues I'd say I did enjoy the beta from what I played. 7.5/10.
At the same time, very skeptical about this game's readiness for release. This is a serious problem. Have not logged in once today. Send help.