Hi, I was wondering if I could get some suggestions as to which spells I should be preparing. I am pretty new to 5e and I keep feeling as if I am always picking the wrong spells. I was hoping I could get some pointers as to what I should always be picking no matter the campaign. Previously I have tried to guess if we were going more of a social/rpg kinda evening or if it would be more battle heavy and preparing accordingly. It hasn't been working that great for me so far. 

My character is a level 8 Gnome Diviner and these are the non-ritual spells that I have in my spell book. 

1. Feather Fall, Fog cloud, Grease, Mage Armour, Magic Missile, Protection from Good/Evil, Ray of sickness, shield, sleep, Tasha's hideous laughter. 

2. Detect Thoughts, invisibility, levitate, magic weapon, mirror image, spider climb, suggestion

3. counter spell, fireball, haste, hypnotic pattern, major image

4. Banishment, Dimension Door, Otiluke's Resilient Sphere, and Watery Sphere

I have a bit of gold at the moment and have been thinking about picking up misty step and polymorph. Any other must have spells that I might be missing?

Again, thanks a lot for any suggestions! :D 

You hit on the huge challenge with playing a wizard. You can’t prepare every spell that you have every day and sometimes you prepare the wrong spells, but you’ll get better at that with practice. 

My suggestion is try to always prepare a few multi-use spells and pick a few go-to spells so that you usually have something available that will be useful. You’ll never have a perfect spell mix for any encounter, social, exploring, or combat, but you’ll always have something available for most encounters. And then switch up a few spells based on what you think you’ll need that day. 

Here are my opinions. Treat them as such.

• You already have Dimension Door, Misty Step is a shorter range teleport. The only reason to pick it up is because it’s a bonus action spell. 
• Prepare either Grease or Fog Cloud most days, but not both. They’re both 1st level area of effect control spells. 
• Sleep isn’t very useful to you at 8th level most of the time. It is sometimes, but not often. 
• Prepare either Tasha’s Hideous Laughter or Ray of Sickness most days. They’re both 1st level, single target control spells. 
• Levitate is a multi purpose spell. It can be used for exploration, it can be used to keep you or one of your allies out of melee, and it can be used to keep one of your melee opponent’s immobile so your party can turn them into a pin cushion if they fail a save. You did roll a 5 or 6 on one of your daily Portent rolls, right? That can ensure a failed saving throw.
• Banishment is great when your target fails it’s save. Especially the opposing spell caster who is hiding behind a meat shield made up of living melee based opponents. Picking between preparing it and preparing Levitate is a tough, tough choice since the two spells take different types of opponents out of combat while you mop up their allies.  

I hope this helps a little bit even though it isn’t, “Do this, it’s the best thing to do.” 

Okay, you get to pick 8 + your Int modifier, which I'm going to assume is +5.  Counterspell and shield are obvious, as is mage armor.  I would say that the other 10 depend on what you want to do, but, well, 10. 

The ones that require concentration are fog cloud, protection from evil and good, Tasha's hideous laughter, detect thoughts, invisibility, levitate, magic weapon, spider climb, suggestion, haste, hypnotic pattern, major image, banishment, Otiluke's resilient sphere, and watery sphere . . . which is, of course, over half of your spellbook.  This is a bad thing because you can only concentrate on one spell at a time and your concentration can be broken by adverse conditions (primarily, getting hit). 

I was going to do several more paragraphs of analysis, but instead I'll just point you to this guide. 

Edit: One more thing.  When you level up, learn animate objects and Leomund's tiny hut.  First other chance you get, learn find familiar--I recommend an owl. 

Thanks for the suggestions Tim, very helpful! 

The reason for picking up Misty step is for the bonus action aspect of it. But I guess it could be too much if I had both of these. 

I have also been using levitate a good bit as a multi purpose spell and I have found it quite enjoyable. 

I will be remembering to pick more of the level one spells like you mention. 

Thanks for the suggestions Matthias!  I have already been looking at the guide you linked and used it quite a bit.  I guess I have just been picking too many concentration spells

I do have quite a few other spells though but didn't think to post these since they are rituals, but I can post them under. 

Level 1: Alarm, Comprehend Languages, Detect Magic, Find Familiar (I have an owl), Identify
Level 2: Lemund's tiny hut and water breathing. 

Misty Step uses a 2nd level spell slot and a bonus action while Dimension Door uses a 4th level spell slot and an action. Misty Step costs less, especially in combat, but it’s range is only 30’. I tend to end up with both spells plus Thunder Step in my spell book when I’m playing a wizard but I rarely prepare more than one of them at a time and I learn them “in order”.

I love your selection of ritual spells!

Thanks again! :D

Are there any other spells that you find you use very often and that you find work nicely?

I’ve found that I’m more effective as a utility/control caster than as a combat caster. I keep a few combat spells prepared, and I also have at least 1 cantrip that requires a saving throw and 1 that requires a to hit roll, but I’m more effective at utility than I am at doing damage. It’s my mindset and how I think, I’ve also played with people who are blasters supreme as arcane casters and they just do insane amounts of damage so you’ll have to find your own path. Treantmonk is almost 100% a utility/control caster.

I try to keep a combination of area of effect and single target spells prepared because there are times when you can’t use an area of effect spell other than Slow because your party is in a chaotic melee situation and if you use an area of effect spell you’ll hit your party with friendly fire. The exception to this is when one party member who has Evasion or Resistance to the damage type of the spell that you have prepared is alone in the middle of a group of opponents and says, “Hit me!”. Then you hit him with your area of effect damage spell. 

You will usually need something to do while you’re concentrating on spells, so keep non-Concentration spells and other options prepared. Mage Hand is a great way to use your action to administer a healing potion without getting into melee while you concentrate on Haste or Banishment for example. But that’s also a great time to cast Magic Missile or Ray of Sickness. Or to move up beside someone who wants to escape from melee and cast Dimension Door to get both of you some distance from melee. 

I try to keep a variety of spells prepared with a few things in mind. I want a variety of saving throws to force on my targets; I want to be able to do  a variety of damages (force, fire, acid, etc.), and I want to have some defense spells. I don't think a wizard needs a lot of attack spells. With some variety in the cantrips (such as fire bolt, shocking grasp) and magic missile, fireball, maybe another attack spell, like Melf's, then you could devote the rest of the spells to defense and utility. With a diviner, you want Mind Spike from Xanthar's Guide, which gives you a second level attack spell that lets you take advantage of the Expert Divination feature of your school. Put a higher level divination in there too, like Arcane Eye, and take something else out. I think Invisibility is not such a great spell.