Though it is a bit difficult to draw conclusions from the screenshots, it appears as though the top area is a menu automatically created by WordPress when no other menu is present. If that is the case, creating your own menu without including a link to your “Welcome” page would solve this.
The second one might be part of Breadcrumbs. If so, check whether there is an option in your theme to disable the feature.
The third one looks like the page’s title. To remove it, as mentioned by @toscho , you need to find the template which generates it.
If, as you mentioned, you want to remove these via CSS (not the best option, but better than nothing), you can use your browser’s Developer Tools to locate the elements and their classes, IDs, etc. You can access your browser’s Developer Tools either by right clicking on the element you want to check and choosing “Inspect Element”, or by pressing the F12 key, which will bring out the entire console. After locating the elements you want to hide, use the plugin you’ve installed to add your CSS code, which, in the case of the title, could look something like this (the actual code will depend on your theme) :
.home .entry-title {
display:none;
}