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But, burning hands is great, you quite frequently hit 3-4 enemies with it, and many enemies are weak to fire. I find myself using it even at higher levels. In the many encounters which take place in smaller, tighter areas, your wizard will be in the fray, whether you like it or not. Also for that reason, you'll want mage armor and/or shield. Your wizard won't be much good if she's pushing up daisies. Scorching ray is literally and figuratively "hit or miss" as it requires attack roles. More often than not, only one will connect. At 3rd level, haste and fireball. Both are almost OP.
There aren't many "wrong" spells, just depends on your tactics. So pick the ones you deem most useful and go with it. Some players prefer controlling the battlefield, others go for pure damage, others, like myself, prefer a mix of both.
I haven't found charm person all that useful, mainly because it's limited in what it effects but I also thought it was a concentration spell and apparently it's not. I prefer ray of frost and chill touch over fire bolt for the reasons you mentioned and because it's good to have varied elemental effects to target creatures resistant to one but susceptible to another.
Grease is a good spell at the early levels and unlike sleep it stays relatively useful at higher levels, though by that time you should have spells like stinking cloud/cloudkill which are better. Sleep is outstanding until the enemies you're facing become immune due to hit dice. I guess you could cast it as a higher level spell, but it's only +1 HD per additional spell level. Edit: it's +2 HD/level; maybe it's worth testing to see how a lvl 3-4 sleep spell does against stronger enemies?
I take thunderwave over burning hands or shocking grasp as my "oh no there are enemies attacking my wizard in melee!" last resort, but I rarely use it over either magic missile or misty step in those situations.
But assuming you will only have one arcane caster in your party and it's a standard wizard here's some I usually take on level-up:
Cantrips: light, sparkle, ray of frost, annoying bee, chill touch.
Level 1: magic missle, grease, shield, identify (learn, then cast as ritual), sleep (unlearn later, but useful for the first few levels), thunderwave, longstrider.
Level 2: misty step, scorching ray, invisibility, silence, shatter, pass without trace, blindness.
Level 3: counterspell, stinking cloud, haste, fireball, slow, fly.
Level 4: black tentacles, blight, dimension door, ice storm, phantasmal killer, wall of fire.
Level 5: cloudkill, cone of cold, mind twist, insect plague.
There are other useful spells and you'll likely have found scrolls you can scribe into your spellbook by the time you start selecting second and third level spells, freeing you to take spells that are more useful to specific situations - feather fall, knock and/or protection from energy for example.
I'm probably missing something but I hope that helps.
rdpeyton's list is pretty solid, but I'll cull that to what I'd consider the bare essentials for a wizard at lower levels.
Cantrips:
Light - If anyone in your party doesn't have darkvision, this is the easiest way to get a source of light.
Chill Touch - Ranged touch, piddly damage but blocks healing, including regeneration. You'll want this.
1st level:
Mage armor - Unless you have another way to boost your wizard's AC (court mage with medium armor), you're going to want mage armor. It's a good value, too - eight hours long, no concentration needed.
Identify - You don't need to actually prep or use a spell slot for this, just have it on your list. You can then ritually cast it to identify your items.
Grease - Amazing utility, as one spell lets you effect multiple enemies for much of the battle, slowing them down and rendering them vulnerable to melee attack. Prone enemies do get advantage against ranged attacks, so if you're running an all-ranged party skip it.
Sleep - Good at very low levels, falls off later. You're a wizard, though, so that's irrelevant.
Magic missile - Somewhat pointless at low levels, but increasingly useful as a reliable way to finish off weakened enemies or get damage on targets with weird resistances or immunities.
Shield - Like magic missile, this gets more useful the higher level you are.
2nd level:
Scorching Ray - decent damage for the slot, but requires attack rolls.
Flaming Sphere - Concentration, but you get to use it all battle for a single spell slot
Misty Step - Another "gets better later" spell, as once you don't need low level spells for damage you can use them freely for utility.
3rd level:
Fireball - OP by design cuz 5e is bad. Still, you're gonna want it.
Haste - Really good if you have a fighter-type to slap it on and get extra mobility, attacks, and AC. Probably the best use of your concentration much of the time.
Counterspell - Do you like getting shot with lightning bolts? If no, take counterspell. If yes, take lightning bolt instead and shoot your own team with it.
I'm not big on Slow, because it's a concentrate effect but they get constant saves against it. Rarely sticks for long but costs you a spell slot, actions to cast, then concentration in exchange for a short debuff that may not matter.
Generally, don't overload yourself with concentration spells. You want to have at least one spell prepped per level that isn't a concentrate spell, since you're only able to keep one up at a time.
Det Magic
Identify
Feather Fall
Shield
Jump
Magic Missile
Cantrips:
Sparkle
Dancing Lights
Fire Bolt
Chill Touch
I generally make a High Elf my Wizard, and I boost their DEX in character creation. They can use a bow to inflict damage from range. The FF and Jump will come in HUGE handy in terms of actually playing the game.
In Lost Valley comprehend language can get around no one in the party speaking giant which can come up depending on how you deal with some you meet. Detect magic became more useful when they change it to merchants needing to know things where magical before they would identify them. Wizards still don't really need it as using identify as a ritual gets around the need for detect magic.
True. I remember the first time I played through Lost Valley was in a multi-player session. No one took giant as a language so the wizard that had comprehend language became very useful in certain situations.
I filled my wizard's spellbook not long before they got to level 7 (or 8, I'm not sure), and then discovered that I cannot level-up the wizard if they cannot write their new spells somewhere.