just a few things to add/clarify. "live" sand is just a term for sand with bacteria, personally i don't trust buying it as live. after you add sand to the tank it will only be a mater of months before your sand is more "live" then any you would buy. live rock is the same except i trust the "live" label far more, depending of course were you get it. any time you add live rock to your tank you must take into account that there will be some die off, but generally its not too bad. you can get base rock to prevent this small ammonia spike. base rock will become live rove in time.
ok, on to filtration. it is important to understand what the filter does when deciding whether or not it is necessary. hob filters usually have an area for biological filtration( aerobic bacteria), mechanical, mechanical, and chemical. usually carbon is useless unless you need to remove something like medication. mechanical can be useful depending on the setup, i found restricting flow in a reef system can cause problems when you start to collect livening organisms like plankton and they die and cause unnecessary ammonia in the tank. in a fish only they may be somewhat useful, but i dont think id personally worry about it. personally i would just get a good pump to pump about 200 to 300 gallon per hour, and let the live rock do the biological filtration. Were there is oxygen available there will be aerobic bacteria. these will take care of your ammonias and nitrites. if you have a proper amount of live rock, you don't need to have a hob filter at all.
as for nitrates, most systems aren't equipped to handle them. this is why you hear talk of nitrate spikes. the only way to really handle nitrates is with anaerobic (no oxygen) bacteria. normally i would just suggest an addition of a mud filter, but in the spirit of keeping with the simple fish only system i would instead suggest to simple add more sand. probably about 4-5" with mounding it in the back to be more should give you a balance of anaerobic conditions while still leavening some space left in the tank. it probably sounds like a lot of wasted display space and needless expense, but i promise you there is no better way to take care of nitrates in your setup. you may even be able to skip some water changes once your substrate matures.
as far as the substrate to use you will need fine substrate to restricted the oxygen. you can certainly mix coarse with it, some burrowers like this option, some don't, but you will definitely need fine substrate as the base.
you can take the nitrate elimination one step further and introduce an algae to your tank. there are many species of beautiful macro algae that will not only add to your tanks appearance but can do a wonderful job keeping your water parameters ideal, as well as out compete some of the pest algae that often trouble fish only systems. just keep in mind that some species can grow pretty fast, not necessarily a bad thing, the faster they grow the more they are cleaning your tank, but its something to be aware of. probably a good idea to make a new post if you decide to go with macro algae asking about the specific species your considering.
so basically what id put down on your list of things to get; a strong pump, more aragonite, and maybe a little more live rock or base rock if needed. a skimmer is always good when you don't have a mud filter, but you may be able to skip it. i would say let your sand bed mature, 4-6 months, and see.