Good for you! My thoughts are that it would be cool to mix pure "learning" exercises with "portfolio" pieces.
The learning exercises might consist of simply coding up a few simple exercises in the areas you have listed. Pick a decently rated text and do a few problems.
The portfolio work should probably approximate working systems (e.g., mini-products). Since you are interested in web dev, throw together some working web apps that have full front-to-back-end stack.
Another option, and this one worked out well for me personally, is to take advantage of a cooperative education and internship opportunities. You'll gain a perspective on coding in the "real world" that you'll never get working on personal projects.
Thanks, this is good advice. I'd consider an internship, but I'm concerned that most of the good ones wouldn't accept me since I'm still lacking in several areas. I'm willing to put in the work to learn quickly on the job, but I feel like I'd probably fail a technical interview.
Trust me, companies recruiting for internships know that you don't know anything yet. I interned and did co-ops after my first sophomore semester. Probably more than half the purpose of big corp internships is to fill the recruiting pipeline. Startups and small companies may need a more "ready to hack" person, but you'll find that out quickly.
Another quick observation, not meant to discourage at all - we all lack in several areas. Always. I think for hackers, one of the only skills that matters is that you have established your ability to learn how to do details on the fly (like pick up a new language) while holding onto the fundamentals that help you stay productive and organized.
In other words - hang onto the "I have so much to learn" attitude, but be confident in your "getting things done" ability along the way.
The learning exercises might consist of simply coding up a few simple exercises in the areas you have listed. Pick a decently rated text and do a few problems.
The portfolio work should probably approximate working systems (e.g., mini-products). Since you are interested in web dev, throw together some working web apps that have full front-to-back-end stack.
Another option, and this one worked out well for me personally, is to take advantage of a cooperative education and internship opportunities. You'll gain a perspective on coding in the "real world" that you'll never get working on personal projects.