Sample data is what I posted in the first message in the attachment.
Sorry, but many people (including myself) will not download an image just to look at it once. You can embed it in the post so it is visible to anyone reading the thread:

(Technique described here.)
That looks like a console interface. It doesn't really show the NMEA-like data. I think you can use this interface, but you'd have to program the Arduino to (1) watch for the command prompt with readBytesUntil, (2) send a command, (3) watch for particular fields to come back, again with readBytesUntil.
For non-blocking solutions (i.e., not readBytesUntil), Robin2 has already pointed you to Serial Input Basics. Finite state machines could help, too. Take a look at the Useful Links page.
What model number do you have? If it's the GN or GV 86/87 series, they will emit standard NMEA sentences. NeoGPS is unique in being able to parse the talker IDs, unlike TinyGPS, TinyGPS++ or Adafruit_GPS.
The Furuno devices can also send and receive Proprietary sentences. NeoGPS provides a method to send those configuration sentences from FLASH, saving a bunch of RAM:
gps.send_P( &mySerial, F("PERDCFG,NMEAOUT,GST,0") ); // Disable GST sentence
To parse the proprietary sentences, you can derive classes as shown in a NeoGPS example, PUBX. The Furuno devuces have a lot of capabilities, so I'm not sure if you want to do a lot or just a little. If you just need one thing, it might be quicker to use the very-lean readBytesUntil, followed by a few parseInt calls.
However, if you want to verify the checksums, get several fields and/or avoid blocking, you can't do any better than a carefully configured NeoGPS. It is faster and smaller than all other NMEA libraries. It is even fast enough to run during the RX interrupt, with the special serial classes NeoHWSerial, NeoSWSerial or NeoICSerial.
If you're currently using SoftwareSerial, I hope you realize it's a real CPU killer. If you can use pins 8 & 9 (on a UNO), AltSoftSerial is a better choice. If not, NeoSWSerial is a drop-in replacement that works on any pins and is MUCH more efficient and reliable than SoftwareSerial.
I think you need to decide if you are going to use a console interface or a NMEA sentence interface, and whether you can use a blocking solution (ok) or a non-blocking solution (best).
Cheers,
/dev