I will say that I have almost no play experience with me or anyone in my group playing an Eldritch Knight, but from seeing Arcane Tricksters (which have the same spell progression) played, I'll say: don't think of yourself as a magic-user who can fight so much as a fighter with some magic tricks up your sleeve.
Depending on whether you want to go for a melee build or a ranged and/or finesse build, you'll want to focus on either Strength or Dexterity. You probably don't want to focus on Intelligence too much (I've even heard of some builds that don't boost Intelligence at all, preferring to use spells that don't have saves or attack rolls, but that may not be the best), since spells probably won't be your main mode of attack, since you don't have spell slots to spam damage like a full spellcaster, and cantrip damage pales in comparison to weapon attacks, especially from a fighter, who gets the most weapon attacks of any class. And, even though you generally shouldn't spam spells as an Eldritch Knight, I will point out that Action Surge puts and Eldritch Knight in the unique position of being able to cast the same spell twice on the same target(s) in a single turn, so, once you can cast Fireball, and you really need to make a lot of things dead for sure, you can.
As for spells, you have to pick from abjuration or evocation for the most part, with the occasion few picks from other schools. The way I like to sort out which ones can be taken is
this site, though you can also use the official
WotC app site, which will give you a bit more information about the different spells and includes spells from sourcebooks like Xanathar's Guide, though you'll need to use advanced filters to be able to filter by spell school.
Shield is definitely a good spell to take, since, though you have very limited spell slots, being able to take any attack that would have been a hit and turn it into a miss is invaluable, and getting a significant bonus to your AC until the start of your next turn makes it even better. Being able to stop magic missiles is going to be pretty situational, but very nice when it happens.
Eldritch Knights can cast Magic Missile, but I'm not sure if it's the best spell to take, since it does so little damage by spell level, and is only really good against things that have a lot of armor but not a lot of hit points, or in the case that you just really need to make sure you hit your target.
Fireball, as mentioned above, is really nice, or really anything that can hit a lot of targets and do some damage even if they save (though Fireball is probably the best at this).
A thing to definitely keep in mind is cantrips. Don't go for the most damaging cantrips, as cantrip progression for the most part follows Fighter Extra Attack progression, and your weapon attacks should do more damage than even the most damaging cantrips. Instead, it's better to go for spells with utility, especially since, from 7th level on, you still get to make an attack as a bonus action when you cast a cantrip. So you can use things like Shocking Grasp to take away your enemy's reaction, Ray of Frost to slow someone down, or Blade Barrier to halve weapon attacks. Plus, since the cantrips aren't limited by school, you could take Minor Illusion and create illusions while you fight, or Chill Touch to stop someone from healing or make it harder for undead to hit you, or Prestidigitation to clean your pants after you soil yourself in battle. If you have access to spells outside of the Players Handbook, you can use Create Bonfire to light a fire under you enemy's ass; or Green-Flame Blade to do a melee weapon attack, and, if it hits, do damage not only to your opponent, but to another enemy next to them. Or Booming Blade, which can also be used with melee weapon attacks, and can either be used to keep enemies close to you under the threat of taking lots of damage, or you can use something like the Mobile Feat to avoid taking opportunity attacks (or take them, if you're brave enough), move out of the enemy's melee weapon range, and they either have to stay in place or risk taking damage (doesn't work so great against people with ranged attacks).
I suppose that's a decent enough start. If you want a more in-depth look, you can probably Google something like "Eldritch Knight 5e Build Guide" for more of a breakdown of various spells and such.