If you settle for a mainly ground dwelling species ( the popular beginner species like auratus, tincs, leucs etc.), a horizontal viv is best. I can really recommend Phyllobates bicolor as a beginner frog by the way. It was not love at first sight for me, but they sure are brave and comical frogs that are very hardy and eat almost anything.
I'll give a start for a list of thing to think about
-Vivarium: Second hand vivarium pro: cheap and allready "furnished". Plants are allready grown in. New viv: clean, you can give it your personal touch. All and all I think the second hand fully decorated viv is usually cheaper than decorating your own viv from scratch.
- Water: will you spray by hand (every day or every couple of days)? Or will you spray automatically (more costly but less hassle and easier if you are away for weekends etc.) So: handmister (few bucks) vs. spray installation (hundred bucks or so).
- Food: how are you going to culture the frog food? Do you have a place for the fruit fly cultures in mind? They stink a little, that's why I keep them in the hall way and not my living room for example.
- Temperature: how will you heat the set-up? Heat cable is an option, sometimes the lighting is enough but this depends on the kind of frog and the room temp around the viv.
- What lighting will you use? For good plant growth this is essential and can be a bit costly. I paid around 100 euro's for lights on a 1 meter high viv.
- Offspring: Most hobbyist eventually (rather sooner than later) get offspring. You can house these in plastic shoe boxes for instance or in there own fully decorated viv. This of course depends on your budget and the room you have.
- Ground: you can use a false bottom for drainage made from egg crate. On top of this comes the cocopeat or something similar. This is all reasonably cheap.
- Plants: You can keep this really basic or very fancy; all depends on your creativity and budget. My planting cost me about 30 euro's (but I had a lot of cuttings in there that I got for free).
-Wood for decorating: this will cost 0 to 100 bucks, depending on what you choose
- Background: you can make this yourself with great stuff for instance or you can buy fern tree panels (first option: 10 bucks or something similar, last option can easily be in the 100 bucks)
- Animals: the price of dart frogs is very variable. Some cost only 10 euro's or so, others go for 200 dollar. Roughly stated the cheap frogs are the best beginner frogs that breed the most.
I hope this helps you get an idea. If you're interested, I can send you an excelfile with my expenses that were made for my vivs etc. It is in Dutch, but that's nothing Google translate can't handle