KSP is an incredible game, but it's made even better by the amazing modding community. Unfortunately, it's a bit daunting for newcomers, so I made a list of mods for you to consider! They range from small tweaks to massive parts packs; hopefully, there's something you'll like!

First, a Scott Manley video on installing mods - it's pretty simple and most mods include instructions, but video guides can be helpful anyways:

HIGHLY RECOMMENDED: Minor quality-of-life tweaks

• MechJeb / Kerbal Engineer - These two mods are paired because they provide similar functionality at a basic level, but represent two distinct choices. MechJeb is easily the most popular KSP mod, and for good reason; in addition to giving you info about your craft's mass and delta-V, it adds in autopilot, making banal operations like inserting into a circular orbit as easy as hitting 'enter'. However, a lot of players see flying the craft an integral part of playing the game. If you don't want the temptation of autopilot, Kerbal Engineer gives you all the info you need about your craft without the autopilot.
• Active Texture Management - If you're squeezed for memory - and if you have a lot of part mods installed, you probably are - than this mod will help reduce out-of-memory crashes and such, as well as cut down on load times.
• Joint Reinforcement - If you've played KSP, then you're probably familiar with the problems in making tall rockets - they tend to wobble around like crazy, often leading to annoying structural failures. This small, lightweight mod helps reduce that, making for more structurally sound rockets! Almost necessary, in my opinion.
• Docking Port Alignment Indicator - A useful tool for lining up docking ports!
• Protractor - A useful mod for figuring out rendezvous angles; incredibly useful for planning out efficient interplanetary burns.
• Kerbal Alarm Clock - An easily recommended mod; it allows you to set up alarms for important events, letting you run multiple missions at the same time or safely time accelerate without missing your window.
• Enhanced Navball - Adds little ghost icons to the navball so you don't have to search around the navball for them!

INTERESTING ADDITIONS: Extra content to expand your game

• Interstellar Mod - As a student of physics, any mod that throws around terms like 'Carnot Efficiency' and 'Alcubierre Drive' catch my attention pretty quickly. IM adds an insane amount of near-future tech to the game, from antimatter collectors to fusion reactors to realistic warp drives (!!) as well as introducing a bunch of new gameplay mechanics, like waste heat. Not a light mod by any stretch of the imagination, but if you're bored with vanilla KSP and want to push your career tech tree further, this is one of the first places you should turn.
• Chatterer - Adds some ambient noise to your game! Beep... Beep... Beep...
• Kerbal Attachment System - Just what it says on the box! Adds a bunch of useful systems for attaching things to other things; good for towing, or storing, or doing stuff like transferring fuel without docking.
• Kethane - Adds the ability to extract & refine Kethane into fuel, for creating self-sustaining missions or refueling stations.
• Clouds & city lights - Adds some nice visual touches to Kerbin when viewed from orbit. Makes your screenshots look pretty!
• B9 Aerospace Parts Pack - One of two parts packs I'll recommend, this one focuses mainly on spaceplanes, with some incredible-looking fuselages and drop-dead gorgeous cockpit interiors.
• KW Rocketry Parts Pack - The second parts pack I recommend, KW Rocketry focuses on giving you more options in rocket-building; their variety of liquid and solid engines are balanced well against the stock ones, and also adds fun stuff like fairings and 3.75m parts that are absolutely huge.

REALISM ADDONS: Make KSP MORE difficult!

• TAC Life Support - Adds life support systems to craft, making time-of-flight an important factor in each mission. If multi-year manned missions in a cramped command pod bug you, this is probably the mod for you.
• Ferram Aerospace Research - Adds more realistic aerodynamics to KSP; this makes creating and flying planes much more difficult than vanilla, but also gives you a bunch of interesting tools to better design them!
• Deadly Reentry - Makes it so parts can overheat and explode when entering the atmosphere at high speed and adds heatshields to counteract this, just like real life!

This is list consists of mods I either use or have heard good things about; there's still quite a few more good ones out there! I didn't mention a few that are still in development, like ScanSat and Kerbal Multiplayer, because they're not quite ready for prime-time yet, but checking out the KSP Addons forums will yield all sorts of interesting stuff like that. Also! I'm not sure what will happen if you run all these mods together at once, so try to cherry-pick, at least at first. Most mods should be compatible with one another, though. Happy rocketing!