What headphones are you currently using or you have experience with? the budget you've stated could afford you a suitable amp/dac and headphone, I agree that you could be limited using that dongle @ 130mW, I know the 'Audio Science Review' crew (an audiophile forum) believe that everything can adequately run off a Apple Dongle but I really believe you need more power and headroom,
Fiio K11 desktop amp £120
Hifiman Ananda (orignal) £348
Comes under the top end of your budget, if you go for the Sundara's just make sure they are the 2020 model.
IEMs are another whole ball of wax, I finder them harder to recommend as the tuning of them have a bigger impact on you and potently less tolerable compared to headphones, I love IEMs but find many of them too harsh sounding for me in the upper mids and lower treble region, a safe 'cheap' IEM I would recommend would be something like the Truthear x crinacle zero red (£50), I promise you'll be impressed if it's your first IEM, they've came a long way compared to the earbuds of yesteryear, but be warned, they can be quit addictive, I have about ten of them lying around lol