First of all, welcome to TST!
Don't skimp on the ball, the shoes, the bag, and to some extent apparel. That's not to say you need top of the line equipment, but you should be willing to spend more than the minimum on those things. Clubs are another story; the market is flooded so it's easier to save money on at least part of one's set, for example I used component irons and saved a few hundred dollars despite putting top of the line shafts and grips on them. I also went with slightly older wedges; I want nicer ones such as Mizuno, Vokeys or Edel, but I can't claim the current ones are holding me back. I use a 20$ putter and I make nothing with it, but my stroke is terrible; it's roughly the same oddly shaped chunk of steel as you'd find in top pro's bags underneath the paint. I think going for a nice fitted putter is worth a spend though.
Also if you use a rangefinder, get a laser. I don't care how accurate a GPS says it is, the laser is more versatile and portable. The GPS or app rangefinders are better than nothing but I'm glad I spent a little more money for the laser, found one under 200$. The only downside is a bit of bulk.
Apparel is important, not in terms of what you wear on nice days though. I wear whatever is clean on those days; I spent more on my rain gear, windbreaker, and a good thermal jacket or sweater for the cold. Under Armour is nice to have if you live in a chilly area or play in the mornings. I am a hardcore winter player so I've been known to go out in 35 degree temps with wind and light rain. You don't want to be wearing a trash bag in these circumstances, but if you have a nice gore tex jacket and some layers, and keep the legs and feet dry, it's still playable. On days a little nicer, it can make you downright comfortable when unprepared players are howling about how wet and cold they are. Rain gloves are a must if you play in wet conditions, they make it a lot easier rather than needing to constantly dry off your grips. I don't usually wear a normal glove though, they just cost a lot, break quickly, and don't do anything for me.
In terms of shoes, I haven't tried out a ton of models, but I recognize their importance. I bought a pair for about 60$ that was an older model, and they provide fairly good grip. However, I may go for a spikeless shoe to try them out, such as True Linkswear. They are much thinner and lower profile so you sit lower to the ground, and you can feel the ground better which helps read greens. I look forward to trying on a pair soon, though I'm debating whether to get these or a nicer spiked shoe.
For the ball: I recommend the bridgestone E series, they are under 30$/dozen and are the best balls in that price range. The E5 is my personal favorite value ball, since it has a urethane cover, a rare feature for under 40$/dozen. No matter what the features of the balls say, if the cover is not urethane the ball will not spin very much. It can be "soft" without actually spinning, but the bridgestone E5 is both. The E6 is designed to fly straighter off the tee, and it does accomplish this to some extent while feeling good off the other clubs. It doesn't spin much around the greens but if you're in play more often and you can play short game shots with more roll this doesn't stop you. They both perform well off irons and will stop on full shots. That said, my favorite ball right now is the Nike RZN Black and Bridgestone B330, which are both more expensive and require a lot of swing speed to get the most out of them. I still play the E5 if I don't want to spend a lot and can't stock up on cheap deals online.
Sunglasses aren't too bad an idea, though I wouldn't necessarily spend much. Many people swear by a nice pair of Oakleys or something because they help cut glare and can make it easier to spot you ball or the contours of the ground.
For the bag, I can't really recommend a particular model, but look out for these features:
-Large and plentiful pockets, I like to carry extra clothing, a rain hood for the bag, my lunch, extra drinks, etc. There's something to be said for having a bag that can fit an entire 12 pack sometimes too.
-I use midsize grips, so I have trouble fitting more than 10; they get extremely stuck on one another at the bottom because the bag has so little extra space. I can fit about 16-17 in there, but it becomes a long process to fit them all securely and I tend to leave them on the ground when practicing because I hate wrestling with them. My next bag may be a staff bag or something just for the sheer size. I also use the bag to store my clubs so it is essentially furniture as well.
-The stand and base of the bag had better be sturdy as hell. I replaced my last bag for this reason; it was narrow and prone to falling over, especially when heavily loaded.
-Lightweight is a common buzz word right now, and it's very seductive. Only problem is, many companies choose to make their products with less durable materials to reduce the weight, or get rid of features. Don't let the lightest bag automatically walk out the door with you unless you can really depend on the craftsmanship and quality. Plus many bags are a similar weight right now, within a pound or so in most cases. A sub 4 pound bag is really nice but I wouldn't want to replace my bag every year if it weren't solidly built.
-Comfortable strapping for walking as well as carrying to the car and such.
Lastly, lessons and practice facilities are worth some consideration as well, since they can take more strokes off than anything I've listed.