Estimated File Size exceeds remaining disk- Best codec to export with?

You're looking for a format that supports RGB + Alpha in the Output Module settings dialog box.  Perhaps most importantly, you want to consider where you are sending the renders file(s) and which format might work well for that.

If you'd like a movie file, I recommend QuickTime Apple ProRes4444 with Alpha.

If you'd like an image sequence, I recommend either TIFF with Alpha or PNG with Alpha (TIFF tends to render faster).

For file formats that do not support an Alpha, you can render an RGB pass and an Alpha pass, usually adding something like "_matte" to the filename of the Alpha pass and then keeping those two files together.  Video editors may refer to the "_matte" file as a "Hold Out Matte".  

The next time that you need to create subtitles, consider using Premiere Pro's new Caption Feature (and soon-to-be-released Transcription).  
Captions Workflow in Premiere Pro

https://helpx.adobe.com/premiere-pro/using/working-with-captions.html#captions-timeline

The next time that you need to create lower thirds, consider using After Effects' Motion Graphics Template option.

Create Motion Graphics Templates

https://helpx.adobe.com/it/after-effects/how-to/create-motion-graphics.html

It's probably worth noting the following:

• Subtitles are often delivered in a text file format like SRT.  There's a wide range of caption text formats.  Something I really like about services like Rev.com is that in addition to being low cost you can whichever text file format is needed captions later.
• Lower thirds are usually delivered as stand-alone files (not the full run-time of the edit in which they are being used) as still images with an alpha or video files with alpha.