I hope Xeviat doesn't mind but I found this to be an interesting topic, and I'm a new player also, so I'm giving my two cents also.
I've played about 16 sessions so far, in an established veteran Dungeons and Dragons group (but they had only played one campaign of 5E before I joined).
I'm playing in two campaigns with separate DMs, who differ in magic items granted (one very little at all, one with more), type of adventure game and amount of non-monster XP granted. Typically we have 5 or 6 PCs at the table (once 7, once 3, three or four times we've had 4).
Our games seem to be a bit heavier on the exploration and especially role playing/dialog component than others I've read about. Typically we have two battles for a 4-5 hour session (but they seem to take a long time to resolve), from 1 to 3 fights normally (set as very tough fights according to the DMs). We roll for initiative each round of combat. We also only get one bonus action or reaction, not both.
My observations:
1) Tons of fun, wished I had played before.
2) The 5E rules are easy to follow if you spend time to read them. We use the 3 main books (with the DMs significantly adjusting monsters) which I now own and the book with alternate kits (don't own). The major issues on our table seem to be everyone figuring the correct initiative (which seems easy to me), flanking issues (we play with tape measurers and 1"=5'), and disengaging/opportunity attacks. Note this is only half the group, the other half doesn't have issues.
3) So far I've played an Elven Battlemaster (5th level) and Elven Eldritch Knight (4th level) - they are cousins in my lore (same gaming world and continent). I've enjoyed them both for different reasons - the Battlemaster can pick times to shine offensively and the Eldritch Knight has been super fun with Find Familiar, Protection from Evil and Good and Mage Hand. Especially the Find Familiar spell - so many role playing situations. I've been using Minor Illusion to let the Familiar "speak" to the party.
4) Classes I've seen played - Fighters (mine and Dwarven), Paladins (Dwarven and Human), Rogue (Human), Bards (3 different humans but 2 were one week players and one Half Elven), Cleric (Human and Dwarven), Monk (Half Elven), Sorcerer (Human). The DMs only allow Players Handbook species and no Tieflings or Dragonborn.
5) The vast consensus amongst the veteran players is that the two classes given the most "love" by the developers are Rogues and Bards. In my experience, and looking ahead in the rules, they are given a lot of great things...especially skills and bonus proficiencies. The Rogue being able to get out of combat so easily is huge for that class, and the Bards flexibility in spells and abilities is so useful. One DM plays a Bard in the game he isn't DMing in and the other DM plays the Rogue - they are also the most veteran players (20+ years each).
6) The Fighter becomes a lot more fun with the second attack. Looking ahead, it seems strange to me that the fourth Fighter attack is at 20th level, past Wizards getting spells like Wish and Meteor Storm. A lot of levels between 12th and 20th. My fighters do stand the most damage and I've only had one Fighter drop to 0 so far, between the Parry of Battlemaster, self healing in small amounts, heavy armor, hit points and Eldritch Knight Spells. I do enjoy not being dragged out of combat like some of the weaker party members.
7) At least in our campaigns so far, we've used some of the skills like Perception, History, Nature and Survival the most. Survival has been the number one skill across the board. Sadly my characters don't have it.
8) Our DMs don't like tracking money, so we don't bother with small monetary transactions - we accept that as untracked money. If it was something larger, then we'd have to do math to see if we have 90% of all the gems and money we've come across since the last purchase.
9) The War Priest is very strong with a second attack when your fights are 1-3 per day (we always have a rest before each session). I know they are limited to 4 or 5 depending on the Wisdom bonus, but if you are only having 10-12 rounds of combat in a night, they are great.
10) The Paladins are extremely powerful in combat - I know they'll be even stronger with more spell slots and if we are still only doing 2 fights a night, even if they are 5 rounds (our longest has been a 9 round fight).
11) Tactics make a huge difference - our Monk character usually has one of the best initiatives and wants to charge straight ahead and not wait for the rest of us. This is what leads to bad events. When the party stays together and supports each other, the game is a lot easier (and survivable).
12) As others have noted, a single monster (even if much nastier than the PCs) is nowhere near as hard as a 5-7 pack of enemies with a tougher captain or mage leading them.
13) I personally think the fighter should get something else early...even if it is only a +1 to hit in combat. It irks me that the bard is a +5 to hit (and that is with his secondary attribute), and I'm only a +6 to hit with my primary attribute.
14) Ask away if you have any questions....
