Hey Mike,
I'm a newbie here and to vivs myself, but I'll share with you some of the sites I found informative and inspirational. I also have some opinions and most of whats out there are just that; some happen to be more correct than others. I tried to find ideas that worked well for many and made sense to me.
This instructional journal was really neat as it had a similar false bottom format to what I was trying to make; gave me some confidence to know it could be done this way...
http://badmanstropicalfish.com/vivarium/vivarium.html
Here is another that is simpler and would probably work best for your 10gal.
http://www.amphibiancare.com/frogs/arti ... ottom.html
Sounds like the wattage (17W) would be ok for some tropicals, though bromeliads would appreciate more light, I think. There are lots of bulbs for sale that are meant to grow plants, as well.
I don't think it is necessary to have a misting system for plants or frogs, especially in only one tank of that size. Watering the plants and hand misting seems to work fine. If the ventilation is high, your humidity may be low and you may want to use an acrylic or plastic cover. There are hinged tops and kits available online.
As for a bowl, I would read through some more informative PDF sites and see what you think. There are certainly a lot of good threads here to read through on just about ant subject.
There are lots of substrates used in the hobby, I like the Atlanta Botanical Gardens Mix(ABG). Google it and see what you think. A good drainage layer below the substrate, above the false bottom, is a good idea. As with the other elements in a viv, it's a good idea to see what many others are doing and how the different methods work for multiple individuals and choose the one you think is best.
The cost, from low end to high, could run you $150 to $350 excluding frogs, I think, but those figs are arbitrary - I would start by looking up prices of
everything you'd like to incorporate.
My only advice is to research the kind of frogs you want and see what they require - space, temps, humidity, plants, food, and how many of what gender are compatable. And don't believe everything you read, but a good rule of thumb is that, if you can find the same info about something in just about everything you do read(read a lot!), it's probably ok. Personally, I like to call breeders that I do business with, be it plants or frogs, and see what they think.
Also, look into what kinds of plants you want; many plants that hobbyists are using in vivariums will outgrow a 10g. My tank is 16"H, so it was tough to find suitable plants in the right scale. It's hard to find a lot of miniatures that won't outgrow a tank that size, but it's possible if you look through lots of sites offering plants for sale and make some calls to find out what the
mature size of the plants will be. Some plants you just have to resign yourself to trimming regularly, I suppose.
Lastly, make sure to find out if everything you are planning to use, including plants, is non-toxic.
I hope this helps and I hope others offer you there advice, as well - it can't hurt to gain from as many experiences as possible!!!
This page of links has just about everything you can imagine relating to PDFs:
Good luck,
Mike