New to the hobby back after 5 years

Hi all i am coming back to the hobby after taking a break for 5 years. I had to move and when i moved my tank it crashed and lost everything so gave it up for awhile untill i had a permentant residence.. I need a little help just got my new tank set up, live sand and rock in and the new saltwater. Now im a little foggy on the cycle i have everything running keeping lights off but i do turn them on every once in awhile just to check everything out.. Now the cycling my ammonia is going up its at .50ppm oh its only been cycling for 1 week going to do my first water change tonight.. am i on the right track first is ammonia spike then the nitrite and nitrates spike and once that comes down the tank is cycled? Also i want to have corals again but want a little better lighting that doesnt cost me 500 or more just for one light eventually would like it but just had a baby and cant afford that right now. Any suggestion on a decent cheap light system but still works good i have 2 marineland reef led lights.. oh my tank is a 55gal.. i was going to switch to 75 gal but the one i got the frameing is broke made me really mad..