Any general tips, advice, or anything I can get to make my experience as grand as possible?

A gnome fighter, you say? I'd recommend one of two paths, if the halfling outrider, cavalier and whatever other mounty prestige classes aren't available from the complete books.

If you can play lawful good "Dudley Do-Right" do so. Take a level of cleric and worship a lawful/good or lawful good deity and go the path of the prestige paladin (XP penalty, sure, but you did pick a gnome fighter specializing in saddle-beasts, I think this might come with the territory). This will beef up your mount, martial ability, cleric spellcasting ability and not overwhelm you with a large array of quirky special abilities as compared to many other prestige classes. Basically they reworked the paladin into a class with requirements (also did this with bard and ranger) in the Unearthed Arcana rules. There are even paladin alignment variants in case being the "I'll save you Penelope!" type isn't exactly your style. Each still beefs up your mount and can scale with this prestige class option.

If you can play evil I highly recommend trying out the blackguard. They get an ability much like the paladin's mount, in fact they are much like the paladin at their core except for the fact that they're really wicked and require you to be evil. An advantage here is that they are core - straight from the Dungeon Master's Guide. A bit tougher to qualify for feat-wise, but their mount levels based on character level instead of class level. I once houseruled these as a neutral prestige class and it seemed to work well enough for our purposes, maybe your DM could do the same. For the blackguard, the trickiest part would be having five ranks of hide and peaceful contact with a summoned evil outsider.

Perhaps not the greatest or strongest way to manage your mount, but these options are some tried-and-true ways to have fun with it. Aside from class recommendation, I highly suggest the feat spirited charge. Even without a lance, that's a grand charge. Aside from that, see if your DM will allow the leadership feat so you can attract a cohort who can serve as a mount. I like that you want to keep your riding dog as long as possible (instead of treating this NPC companion as a means to an end like some, ugh), but unless your DM will lift the maximum hit dice cap for him he's not going to keep up for much longer if you don't bring in class abilities or something like to augment him.

Switch to the Unearthed Arcana Revised Ranger

The ranger, particularly the Beast Master ranger, is a notoriously weak class. Effort have been made to improve it in errata, but they haven't gone far enough. You have already encountered just one of the issues with it. The Unearthed Arcana playtest material has a revised ranger class that significantly improves the utility of the ranger companion if you choose the Beast Conclave.

Note: this is only playtest material and not officially allowed; you will need your DM's approval to play it, and it cannot be used in organised play.

The revised Beast Conclave animal companion has several advantages over the Player's Handbook version that increase both its survivability and its usefulness in combat:

• It is proficient in all saves
• It gains an additional hit die for each level you gain after 3rd
• When you get an ASI, so does your companion
• At 7th level, it gets advantage on saving throws provided it can see you
• At 15th level, it gains an ability equivalent to Uncanny Dodge, where it can use its reaction to half incoming damage.

Most significantly on top of being a much stronger and more useful companion, should your companion die you can revive it in a new body with 8 hours work and 25gp worth of rare herbs.

There are a lot of changes in this version of the ranger and it isn't perfect. You give up your extra attack to increase the damage of your companion but if that's the playstyle you want isn't so bad.