Consider this: $300 isn't going to get you a killer bass that you will want to keep forever. You can spend even less and get a good bass to learn on for now. You can pick up a used OLP MM2 that is a Stingray copy for around $100 on eBay. Out of five basses I owned, my OLP MM2 comes in as second best. I like it better than the American Fender P-bass and Rickenbacker 4004 that I also owned. You can add an Aguilar OBP-1 preamp to the MM2 for around $100 (if you do the work yourself and shop around for the preamp) later and bring it up to near original Stingray specs. Mine has a better neck than the P-bass and Rick and it has a lightweight basswood body that really gives it a good tone and takes a load off your shoulders as well. Just because basswood is inexpensive, don't think it's second rate for an electric bass. Think of it as BASSwood. An OLP MM2 fits in any case that will take a Leo Fender bass, saving you money there as well.
Of course, my Spector ReBop 4 blows away any bass I owned before, including the Rickenbacker 4004 and Fender P-bass. It has the Tone Pump preamp made by Aguilar which powers active tone controls. The pickups remain passive and have passive attributes, while the active tone controls will drive any length of cable or amplifier input you choose to drive. The tone control range is much larger than any passive tone control without the weird impedance variations that exist within passive tone controls (I am a degreed electronic technician, so this is not opinion but fact).
I called up Spector to get a user manual when I bought my used ReBop, and got P.J. Rubal on the line (this is common, the co-owner of Spector usually answers all service enquiries, email or phone.....almost unheard of these days). He admitted that the ReBop was his favorite out of all the Spector basses, even though it was the lowest priced of all the USA/Euro models. Why? Because the combination of alder body, bolt-on maple neck reinforced with graphite, and aluminum locking bridge gave it a punchiness of tone that no other Spector bass had, outside of a USA bolt-on Spector of similar construction at a much higher cost. Imagine if you had a P-bass that had the range of tone of the best modern basses, or a J-bass on steroids with quiet humbuckers. That is a ReBop.
I got mine for a lowball $404 bid on eBay (with gig bag), and I was shocked at what I got for my money. It blew away the used Rick 4004 I paid $800 for. I recently saw a used ReBop in excellent condition with case go for $585 on eBay, and it was a beauty. Workmanship and finish on a Euro Spector is definitely in the boutique class. The lowball price on a Euro ReBop is $1600-$1700 new, without case, and worth it. The prices seen on used ReBops qualify them as a steal. All Euro Spectors are built from neck blanks made in the Saugerties, New York, workshop. They are the same neck blanks as used in the USA Spectors. The craftsmen in the Czech Republic factory are some of the best in the world, and Euro Spectors are fully comparable to Warwicks made in Germany at 2X the price. Don't take my word for it. Look up some owner reviews.
Spectors have a tonal range that is awesome. Just because they are a favorite of the heavy metal crowd (like Rex Brown of Pantera), I think they have gotten a skewed image as to what they are. Leigh Foxx of Blondie has used a Spector for years, so listen to some of the later Blondie videos on Youtube. Also, my ReBop neck hasn't shifted a bit in the 8 years I have owned it. Do not underestimate graphite reinforcement in a bass neck.
So my advice is to pay less than $300 and find an OLP MM2 (4-string) or MM3 (5-string) while you search for your ultimate bass, or save up about double that amount and buy a used Spector ReBop or Euro neck-thru that will put you into a boutique class bass that costs about $3000 new from most boutique bass manufacturers. Spector is going to be around for a while, and their service is legendary.
Schecter and USA Peavey were also on my short list when I bought my ReBop. Owners of those are also in near universal approval when you read lots of reviews.
Also, learn to do your own setups. An OLP MM2 and a Peterson VS-1 virtual strobe tuner can give you a perfectly setup bass. You can easily get both on the used market for $300. Learning how to setup a bass or guitar is NOT rocket science, and I had rather do it myself and have it perfectly suited to myself. You have to do a setup check and adjustment EVERY time you change to different type strings, and running to somebody else every time I need that done is insanity since I am not a rich rock star with my own bass technician. A cheap OLP MM2 that is properly setup will beat anything else that isn't.