Well that sounds about par for the course. I have a regular group that I DM for since 2009, and your player archetypes sound pretty familiar to me. (And yes, those are the real archetypes, not what is described in the DMG).
Don't worry so much
First off, don't worry so much. From your post, it seems like it's going ok. The important part is that you have fun. If the group has fun, there's not a big problem, even if you as a DM might feel you are doing stuff wrong.
Talk about it
After a session, or maybe during a coffee or smoke break, ask the players about these topics. What do they like, what do they dislike? How do they think the game can be improved?
If everyone says it's fine, great. If not, I am sure they have some suggestions for improvement. I do this after every session, sometimes for 3 minutes, sometimes we discuss this for half an hour or more. It really helps.
Play to the player's strengths
If a player or his character is good at something (and everyone has has a speciality), give him or her a chance to use this strength. So the rogue player is inventive - give him a chance to use his wits. What I do is that I generally prepare some specific additional puzzles or challenges for them. I think the best way to integrate those is if you have a fight and at the same time some additional pressing matter that people have to attend to, either with some skill checks or just with good ideas. So maybe while the party deals with the brunt of the attackers, someone must slip through the enemy ranks and disable the ballista before the city walls are down.
Help your players
So the ranger treats this like a video game, but is not pro-active enough. Well, he doesn't have to go shopping. Drop some loot for him that is a part (one third) of a magic bow. Maybe a bow string made out of dryad hair? This should awaken his video gamey instinct to collect all parts, involve him more into the story and finally lead to him getting a better bow.
Some answers on this board stress how important player agency and pro-active players are for the game. I am not sure I fully agree with this. Some people are just naturally more passive, and if you can help them so they have more fun and everyone has more fun, just do it.
Use mechanics to cover the player's weaknesses
For the wizard - maybe propose Sense Motive, Gather Information or similar (Insight in 5e) checks when you feel he's missing something. If he succeeds the check, give him a hint. Like this, you can use the character's strength to cover the player's weaknesses. And after a few successes, it is likely that the positive reinforcement will lead to the player doing this on his own more often.
A similar thing about this assertiveness: Have a friendly NPC cast a spell him, or maybe an enemy a curse, and tell him how this makes him feel more assertive, mighty and filled to the brim with power. Sometimes this helps such players to slip into a role they would not otherwise take on.
On the other hand, specifically this is not really a problem in my eyes - a nerdy shy wizard doesn't seem so out of place.
Offer help with their characters
So this is a two-sided sword. It might be a great help, but can also ruin a lot. Make sure the players want and appreciate your help with their characters before doing anything. You really want to avoid messing with 'their guy' if they don't want you to. But if done right, it can be a great help to certain players.
One of my players is like your barbarian player. Doesn't like to read the rules, but is very enthusiastic and a great addition to the game. Before a new campaign, I generally have a skype conf with him and discuss the background a bit and what character he wants to play. Then I build a character for him, send it to him and we discuss some changes he usually wants. Once we have a character he's happy with, I make him a nice colourful character sheet in Numbers with all the important stuff up front. This worked out very well. It allows him to focus on the game, and not worry about details or picking whatever CharOp stuff from way too many sources he's not interested in, while still playing his concept and being on a similar power level as other players who are more into optimising.
Allow them to rebuild or change characters (within reason)
Sometimes, a new player might choose a character that doesn't really fit his play style. Might be the wizard player would be happier with a sorcerer - new players tend to fare better with the simpler approach of having a few known spells instead of building a spellbook and preparing their daily prepared lists.
The system
Finally, maybe D&D 3.5e is not the ideal system for players who don't read up on the rules themselves. If your group is open to change the system, I can suggest two options:
D&D 5e. While similar in many respects, it has one advantage: A lot of stuff is just way simpler and easier than 3.5. While 3.5e is my personal favourite among all D&D editions, for my main group, I have switched to 5e, and we haven't looked back.
Games with far less rules: Dungeon World or Fate come to mind. I have played them, and had fun, but for my group, it was not the right choice. We like the miniature battles and everything around that. But those are certainly great games.
And, in the end, the evil master plan
Of course, all this cuddling and making players happy only serves one goal: to make them experienced enough so you can start being a true evil dungeon master. Once they know the system, know their characters and have a fair chance to survive bad things, the fun starts: Poison, traps and and horrible dismemberment. It's no fun punishing them if they have no chance to deal with it. But once they have shown they are up for the task, you can start driving the finger screws in, and let them into the tomb of horrors.
Best Answer
For the Record
The user RobertF answered this is the comments back in May and I am placing it here in the answers in order to preserve the information.
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