Title says it all, I've used a DSLR before (i'm still fairly new to it all) but now i'd like to invest in one. Do you think the Nikon d3300 is a good start or is there a better camera around the same price?
The Nikon d3300 is a perfectly good starter DSLR. To compare other options take a look at the Canon t5i or the Sony a5000.
All three of these cameras are around the same price point and capabilities. There are minor differences--for example the Canon has a tilt-swivel LCD, the Nikon and Sony don't, but the Nikon and Sony have a slightly better dynamic range.
What would be the deciding factor for me is looking at the higher end cameras from these manufacturers (with the same lens mounts as these models) and asking yourself what you would buy if you had more money. The reason for this is lenses. For a low-to-mid dslr the glass is more important than the body. A $500 body with a $1000 lens will usually shoot better images than a $5000 body with a $150 lens. As you upgrade a dslr body the lenses come with you, so, ultimately, you want to figure out which manufacturer to buy based on higher-end cameras for future upgrades and bringing existing glass with you.
I'm a Canon shooter, but if I were starting today, I would likely go with Sony because of the insane low light shooting of the a7s and a7sii.
Canon for Magic Lantern. Focus peaking, focus pulling, live histogram and waveform are things that I use the most. Focus pull/rack focus is a huge one, literally perfect everytime if you have static scenes/marks for actors.
Honestly, the quality of the other cameras isn't really something to brag about, you need good lighting, but I've used Nikon D5500 (same price as my Canon 600D at the time), and my friend bought that one. It looks way better on his camera in low light, but he's got none of the Magic Lantern features I got.
The Sony's I've heard are fantastic, but I have no experience with them.
Photo taken with my (low end) phone.
Red means that those areas are overexposed, so there's no detail there, and you can see the histogram on the right, which you can make it a bit bigger than that, but I find these two features very useful. If other cameras have them as well, then go with any of those, better option for picture quality in my opinion.
My Canon suggestion:
Canon T5i: https://www.amazon.com/Canon-EOS-Rebel-EF-S-18-55/dp/B00BW6LWO4/ref=sr_1_4?s=photo&ie=UTF8&qid=1474368700&sr=1-4&keywords=canon+t5i
Then perhaps a 28 or 30mm lens to go with it for a close to 50mm as possible (the included zoom lens is fine) after the crop factor has been included.
Have to echo what Triem23 said.
The glass is where its at, no matter the body or brand. A sensor is a sensor (yes I know everybody has "secret sauce" to massage the image). You want to seriously consider shelling for a good lens as part of your yearly budget.