but I know that i'm going to need a telephoto lens
No... no you don't... reel in the GAS... there is very little in life we truly 'need'.. apart from a little self realization to recognize how often we 'promote' things we may 'want' into things we kid ourselves to believe, we 'need' before the sales-men add to the conviction to get their commission.....
Back up.... your comments critasising the borrowed lens, I suspect you really aren't qualified to make, and more, I would hazard a pretty big guess isn't all down to the lens, but your expectations and skill.
Using a bridge, you have the wonderful cure-all of a micro-sensor, that gives enormous potential 'zoom' due to the enormous crop factor; but a lens is a lens, and it does't care how little or big the sensor is.
My 120 Roll-Film 'medium format' camera, the negative (sensor!) is 6x9cm.... the 'normal angle' lens on that sized focal plane is 105mm, on a 35mm film camera, or 'full-frame' DSLR that would be a telephoto in the 'portrait' lens range. On a Crop Sensor APS-C DSLR, that is quite a long telephoto.....
Checking the specs for your Sony, suggests it has a 'true' focal length of 4.5mm to 220mm; the enormous zoom X-factor provided by it having such a minuscule focal length to begin with.....
Now, I have a 4.5mm focal length lens for APS-C; on that size frame, it's a 180 degree FoV 'fish-eye', and whilst it is an AF-Lens that is significantly 'redundant'; at such a short focal length the Depth of Field, or front to back focus 'sharpness' is enormous and with a close focus distance of only about 20com, the depth of focus at almost all apertures is almost from the front of the lens element to infinity....
THIS incredibly 'deep' Depth of Field from very short Focal length lenses, makes them appear incredibly 'sharp'.. and it provides an enormous tolerance for focus error or inaccuracy.... something they rely on with micro-sensor cameras to compensate for rather less accurate lens 'movements' to keep costs down, and the specs up.
Now you are using an APS-C DSLR, that with larger sensor does NOT have that incredibly deep Depth of Field 'sharpness' nor the tolerance on focus accuracy.... whilst the DoF 'focus fade' from sharp focus to 'out of focus' will be a lot more gradual and give the appearance of 'softness'
Larger format cameras are a lot more demanding on the operator to use; they don't do as much for you, you really have to learn to exploit them.
Back to needs and wants......
Once upon a long-long-time ago... the leap you have just made from a consumer compact to enthusiast SLR was likely from a 110 cartridge camera to an entry 35mm SLR. The 110 cartridge instamatic probably had a fixed, mild wide angle lens, the entry 35mm SLR likely came with a fixed 'normal angle' 50mm on the front... and in a similar situation to you, probably 'given' that entry level SLR, we could't afford to buy a large number of accessory lenses that the thing could take! Comparatively, they were probably 3x the cost lenses are for modern DSLR's and they were likely fixed length 'primes' or very limited range, possibly only 2x Zooms!
My first SLR was a 2nd hand Olympus OM10 gifted to me by my Dad when he bought a Pentax.. and I was rather wowed when I saved up to buy a second hand 35-70mm 2x 'short' zoom for it two years later....
The modern entry level DSLR, with 'kit' 18-55mm lens, is comparatively like almost EVERY toy in the shop AND all the film! when I was starting out.
In the camera you have shot-by shot variable ISO, and the option to shoot in B&W or colour; and you don't have to pay for the film, or the processing..... you have an inbuilt popup flash, which was an add-on accessory in days of yore, and that lens? 18-55mm? Well, that is the 'equivalent' of aprox 27 -82mm... I spend years looking for something wider than 28, that I could actually afford for my OM... that really was about as wide as you could get without paying very big money.
BUT it was these 'limitations' that TAUGHT... we had to learn to frame with our feet; get creative, get interactive and put the camera where best to get the subject best in the frame, and if it was a bit small, accept that, and make the most of it....
A-N-D..... big zoom is a one trick dog. Filling the frame with subject, cuts out clutter; it delivers instant 'impact'... but that is about ALL it delivers; cutting clutter, it also cuts context, and after the initial wow factor big zoom shots often lack a lot of interest.... and there in lies the learning..... with less zoom you have to LOOK for the interest; find what it is in the scene that explains the subject; gives it 'context' meaning relevance, and then learn to frame NOT just to chuck it all away but include the bits that most explain the subject, and 'add' to the shot, and give it 'interest' that holds viewers attention, rather than just grabs it.
This is a big leap.. and one NOT to be found in the camera, its settings or accessories!
Say it often enough but COMPOSITION, COMPOSITION, COMPOSITION!
Very easy to look at the gadgets and convince yourself that you 'need' another bit of kit to get the shot you hanker for.... and very very very easy after that to get locked into an ever decreasing circle, chasing the gadgets to do the job, rather than applying a with a bit of technique, or a little imagination and not doing 'quite' the job you had hoped, but looking for a different ways about; a 'different' angle, an alternative perspective, rather than the cliche...... and THAT is the 'art' of photography.....
A-N-D.. after almost forty years of the game, chasing more reach or chasing more wide, and 'now' pretty much having as much of either as I ever dreamed of..... that 'art' still eludes me FAR more often than gadgets....
In your enthusiasm, with a new camera, that has so much more possibility, the impulse to explore it is understandably enormous..... BUT! Take a step back; turn the frustration of what you 'cant' do ts head, and instead, look at what you CAN do.....
Go look at photo's by the old masters, taken with fixed lens plate cameras! They didn't have zoom lenses; they were lucky to have interchangeable lenses! They didn't have variable on demand ISO they had glass plates they probably had to prepare themselves, with an equivalent sensitivity of maybe ISO25! They exploited the hardware at their disposal, and made masterpieces with it.. because THEY were masters.... not because they had all the toys n the toy-shop to hand!
Go look at the photo's you have taken.. find the very worst.. what was wrong? What caused that abomination? The Camera? Or YOU. Now look at your best shot. Same question; what made t good? The camera? or YOU?
Its NOT in the gadget in your hand; its in your head as to how to make the most of it.
So? What to do? Waste sunlight NOT taking photo's because you don't have enough 'zoom'? Or get out there, like the old masters and try make the most of what you got?
Go look at scenary to take photo's of, not at google looking at specs and tests of hardware!!! THAT is where you'd do your learning, REAL first hand learning; not gathering second hand scentific data!!
Its the photo that matters, not the hardware that was used to take it! Judge your results by that, not what the pundits say about line resolution or edge abhorations and sluff like that!