Hi Micah,
Greg gave a good analysis of the financial considerations and the comfort/safety factors for buy vs own.
RAWalker did not overstate the importance of fit in an exposure suit and I will build on exposure protection a little.
DaleHall’s advise to try renting different type BCs is solid I will add some additional advice on BCs.
And as Lerpy stated do not “cheap out on regs”
I see you are from Washington State. My first consideration would be where you will be diving. If it is all local you will need heavy exposure protection (perhaps a dry suit) and that will impact the type of BC you need and the amount of lift required. If you intend to dive primarily on tropical vacations than lighter exposure protection and a lighter (travel) BC is more appropriate. My first purchase would probably be exposure protection including a hood or beanie. In a wet suit the most important feature in my opinion is fit as RA advised. The more comfortable you are diving the more you are likely to dive.
I would not be in a rush to purchase a computer for a couple of reasons. Being a new diver you probably will consume more air initially and thus limited bottom time and less nitrogen buildup so diving from the charts may not significantly limit your bottom time. Also I think really learning to use the dive table is still a good thing. If you plan on doing multiple dives over multiple days like on a vacation then investing in a computer is a good idea and if you are doing multilevel profiles they can significantly extend your “safe” bottom time. Even if you are not nitrox certified I strongly recommend that you make sure to get a nitrox capable computer for future use. Most computers now are nitrox capable with only the cheapest lacking the capability.
For a BC you may want to consider the type of diving you will be doing also. The back wings do help you to orient face down underwater but can be less appropriate if you intend to have one side down like when exploring a wall or when back down such as when scanning the surface occasionally. The amount of lift will be impacted by the exposure protection and potentially by your activities as well as travel. I use a heavier back inflation for drysuit diving and a hybrid for travel and warmer water diving (with up to a 5 mil suit).
For the regs I suggest you first consider the availability and cost of local periodic maintenance. The cost tune-up costs can impact the cost of ownership over time. I would also consult reviews on regs to me breaking pressure is a key concern since a lot of my dives are shallow and long.
So I would probably get exposure protection and then decide on rent vs purchase on the other items. If I decided to purchase additional items the BC and regs would come next and a computer later.