IMO you should definitely read http://www.gally.net/translation/kokugo.htm for a review of many monolingual dictionaries available out there. The page is 20-year old but dictionaries don’t update all that fast…
Another thing you should know is that nowadays, enough of these are available online for free, so unless you want them for offline reference, there is no need to spend money if you don’t want to. The big names out there are IMHO:
- Daijirin / Daijisen (very similar contents). Comprehensive, and geared towards modern usage; Daijirin supposedly has more literary examples.
- Kôjien. Supposedly more comprehensive than Daijirin / Daijisen, but more historically inclined (definitions in etymological order).
- Nihon Kokugo Daijiten. Huge, very comprehensive, but dated, both in contents and presentation. Only available in an abridged electronic edition in most places, unless you want to dive into the actual multiple physical volumes.
Kôjien is not available for free anywhere, as far as I know, but you can find Daijirin / Daijisen on various websites, including weblio.jp and kotobank.jp, to name only the two I use most often. I prefer the UI of weblio.jp (it shows the definitions all on one page when you search, instead of having an intermediate step where you need to select which entry you want) but kotobank.jp has more contents. They make available both Daijirin and Daijisen, but most importantly, they recently added the Nihon Kokugo Daijiten (abridged)… which is great if you’re into that kind of things, though you rarely need it, in reality.
If you absolutely want it, you could get your hands on a copy of Kôjien (easiest way is probably to buy a denshi jisho), but from my little experience perusing it, I didn’t get much out of it; the etymology was lacking where I wanted it the most, and the rest was, well, not really better than Daijirin / Daijisen IMHO, for any practical purpose. And also, if you’re looking for old words and usages, weblio.jp also has a classical (kobun) dictionary already.
As far as apps go, I can’t help much, but others will certainly chime in with their recommendations.
P.S.: Note that unlike more proficient people around here, I’m not a regular monolingual-dictionary user. My vocab is pretty limited, and I rely mostly on bilingual ones for a quick gloss, usually. When I do search the monolingual volumes, it’s because I’m looking for something specific (particular usage, etymology, classical orthography, etc.)… so you might have other priorities.