That all being said, what tips would you guys give for a complete beginner like me? The last iteration I have played was PS 0 on the DS, but I have played the original PSO and its continuation, Blue Burst, extensively.
Some of it has already been said in the mentioned link, but I'll add anything I can think of.
Grinding is a lot stronger then it is in other Phantasy Star games, and a lot more forgiving then PSU. Your weapons will double or be close to double it's starting power when you get it to max +10. Your armor can also make a big deal at +10 and it's considerably easier to get it up that high. Armor grind rates are very forgiving, even for someone like me cursed by the Random Number Generator. This will be what helps out once the damage levels get pretty high and stop the nightmare damage some bosses will put out if you're not prepared.
You'll eventually see element symbol, fire, wind, lightning etc on weapons you find. For weapons you intend to use, this is important as it adds a percentage based on it's value to your overall weapon's damage. This can be raised up to 50, (60 on 13 star weapons). and it'll do a bit more (sometimes a lot more depending on builds / classes) if the element you are using affects the enemies weak elements. So you get your weapon to 50 element, that's 50% of the weapon's damage getting added extra. Light and Fire weapons tend to get the most usage, due to all Darkers being weak to light, and a lot of other enemies are weak to fire.
Some of the earlier bosses are honestly the toughest the game has. Vol Dragon, Fang Banther/Banshee, Quartz Dragon can come off incredibly ruthless early on. We've all been at the receiving end of their attacks and you'll get better at them as you learn the patterns, feel it out. Don't let the deaths get to you.
The earlier mentioned by ChickenHunter missions given by Koffee have one added bonus that you may not pick up on right away. They're a few of the only missions in the game that don't change in exp value per your class. For example, at level 1, they offer 15,000 on average, and at level 75, they'll offer the same. Other quests will widely shrink in worth as you go lower. This is good to level a class from 1 to 10 in about a mission turn in. Good to skip a bit unless you really want that early stuff and it may give you an edge. Something to keep in mind.
When you see the unlock Sub-class mission from Koffee. Snag it and work towards it the best you can. Getting the second class is a nice boost to stats and you'll get access to everything but main class only skills, which'll tie in to the final piece of advice. Admitting, there are a few bad class combos that may on the outside seem amazing. But don't feel afraid to ask or theorycraft, as I'm sure people are willing to discuss build advice.
Some classes you'll see "stance" skills. On paper, they may not see seem that good, but this game is really about multipliers. For example, Hunters have access to Fury or Guard stance. You'll be able to activate one stance per class. If you're say Hunter / Braver you can activate a combination of either: Fury Stance or Guard Stance along with Average Stance or Weak Stance. For most classes that have them, the stances are the biggest sources of damage, I've found a lot of people tend to glance at them and seem unimpressed at first.