It all depends really. If you're looking to start getting serious with shooting video, DSLR is probably one of the cheapest ways to get more professional looking video. The cannon T3i tends to be the most recognizable camera, and rightfully so. Since the newer cameras have been coming out, T3i is becoming easier to get your hands on price wise. You'll notice a lot of people that use DSLR when shooting video say the same thing about audio however. Since the pre-amp in the camera isn't that great, you will often get a considerable amount of noise. For this I would recommend looking into an outside audio source such as a Zoom H1 on a boom pole, if you are looking into doing studio shooting. For lighting it's always best to use a 3 point lighting system. As well as having the light completely shut out from the area you are filming in. The reason this is, is because of the color temperature difference in studio lighting that you might be using and the lighting from the outside. It's always best to have one kind of light source, so that is something you will want to consider.
Also, it depends on if you even need softboxes. Do you need to filter out your light? Is the lighting you have now too harsh? Those are questions you'll have to ask yourself as you set up your set. Also, what kind of lighting are you using? Are you using a white light? What is the color temperature of the lighting you are using? I find that when recording studio wise daylight bulbs are the best. They give off very nice white light as opposed to the more yellowish hue that a lot of standard bulbs have.
Something to note if you are getting a DSLR. Generally they are ready to go out of the box (If you know how to use one already) There isn't really anything you need other than stated above to get started. (Other than extra batteries and cards for storage) The kit lenses are fairly good for what you want to do with them as well, so there is no need to really invest in another lens unless you plan to do something else other than Vlogs.