New sensors are quite good. The t3i is good. The only downside is it's APS-C, which means a smaller sensor... shallow depth of field can be tough to achieve with an APS-C sensor and kit lens. ISO is also something that you have less room to play with, but that's actually not a huge deal (some stuff like wildlife photography can really benefit from better ISO performance).
I like the second shot. The first shot I think could've been taken a couple feet back. The black of what you're wearing makes your right shoulder blend in with the rest of your body... adds bulk to your perceived profile, that isn't actually there. The lighting in the first shot is fairly boring. The second shot's lighting is nice (perhaps a tad bit harsh coming from the left side, the contrast between the two sides of your face could be lessened I think just a touch). But still, second shot is quite nice.
You would be surprised how much you can do with a kit lens and a t3i (or similar APS-C budget, 2015-onward camera like a Nikon D5200... Nikon D3200... or anything newer.)
For portraiture especially, lighting is key. It's #1. You get a good lighting setup, and you could use an iPhone and get amazing results (assuming you have some manual control over the iPhone to avoid any drastic in-camera processing). In all forms of photography, lighting is key... but portraiture is where you paint the light onto the subject (or a combination of finding good light depending on the kind of portraiture). In other forms of photography, you find good lighting, plan for good lighting, etc...
I am a huge fan of landscape + portraiture put together. Planned stuff like starscape, or long exposure of many different kinds, with planned inclusion of a person or people.
I don't do a lot of portraiture, but one great tip I have is play with the eyes in lightroom. Don't go overboard, but doing a few different layers of painting of clarity, exposure, sharpness, color, etc changes to the eyes can really enhance a portrait. Don't be afraid to sharpen around edges just a bit too (selectively choosing some softer-looking edges around a subject that could use some sharpening with a brush).
edit - Oh ya I'd say for photo #2, you could have an even bigger impact with a series (3 photos, for example) done exactly the same, but with different poses. It's really easy for a stand-alone photo to just convey... stock imagery. A stand-alone image that doesn't speak to the viewer is just asking to be inserted into some other bigger body of work, and used. But if you added in a couple other photos beside it, it could convey more... something about you. You'd still be demonstrating your work, and technical efforts, but you would be incorporating a story. Each photo in a series can play with the other, providing context that amplifies your work.
This post was edited by Canadian_Man on Mar 24 2017 06:36pm