If the tank had been sitting with stagnant water for a month, there may well be decaying stuff & possibly toxic gas buildup & other things that you don't want.
I would do a total tear down. I would remove all decorations & give them a good scrub in hot water (no soap!). Ditto for the filter - take it apart & clean out the impeller & all moving parts. I would ditch the filter media. <Unless you have a canister & using ceramic beads, in which case you clean & sterilize those for reuse.>
Next, remove the gravel. Put it in a colander & rinse with lots of water. <I would do that outside if possible.> It will be messy, but you want to get as much of the junk out as possible. <If you have sand, you need to do this with a bucket. Fill with water, stir, pour out water & gunk that had been stirred up, repeat .....>
Finally, wash & scrub the tank with hot water. Use vinegar to remove scales & other buildup.
Some people will then bleach everything after cleaning. <1:20 solution> This is good idea if there is a definite infection present in the tank, or if you have a heavy algae outbreak & want to kill everything. You would have to rinse very well after bleaching, and when all smell of bleach is gone, soak & rinse everything in a double or triple dose of dechlorinator.
Bleaching is quite labour intensive & messy, and you risk leaving residual bleach if you don't rinse well (& that would kill your biofilter ... so you have a stalled cycle). In your case, I don't think there is much risk of any nasties left after 1 month, so hot water is prob. enough. Bleaching is optional.
Once everything is cleaned, you can setup your shinny new tank & start cycling. Since you already have a cycled tank, you can seed the new setup with media/gravel from the old. This should greatly speed up the cycling. <Seeded properly, you can cycle in under a week.>
80 gal FW with 30 gal DIY wet/dry/sump.
9 fancy golds, 1 hillstream loaches, 1 rubber-lip pleco (C. thomasi), 3 SAEs, small school of white cloud minnows, planted.