Cruisers are versatile, but they don’t have the plethora of low slots for armor that battleships do, and as a result you must usually choose between having DPS and having armor, on a cruiser. Versatility means, for example, the option to fit an Arbitrator with no guns (just drones), so you can have enough power grid for battleship-sized 1600mm armor plates, but that pretty much requires T2 drones so you can at least do some DPS. But in general, cruisers are skirmish fighters, and if the opponent out-matches you (a room full of battleships in Angel Extravaganza), you need to have two things: high skills so you can overheat everything and squeeze all the performance out of your meager armor and resist modules, AND game skill so you know when to bug out to repair, what targets to kill first, etc.
Battlecruisers are glass cannons. You get more low slots, but all that extra power-grid that you get is going to be taken up by fitting them 6-8 guns/missiles that you’re supposed to fit on these ships. Battlecruisers are not a step towards being a battleship brick tank, they’re actually a step towards being a more nasty hit-and-run cruiser. You lose some of the mobility and smaller size that cruisers rely on for survival against large guns, and you get more DPS, and more low slots for heat sinks / more DPS.
So, because you have low-ish support skills, you can switch to a battlecruiser to do L3 missions (that’s what they’re intended for, so low-ish skills will still work), and as you shore up the skills for T2 weapons and T2 defenses, overheating, etc., try L4 missions for the purpose of learning when to bug out and when to stay. Because, again, your battlecruiser will be a hit-and-run cannon.
EDIT: Also, you signed up for Omega. Wait a couple days, and consider that for the cost of an additional 1 month of Omega, you can get some PLEX and sell them on the market, for close to 1B ISK, which should be sufficient to afford fitting a few battlecruisers or even T3 cruisers. This’ll let you get established and not have to grind ISK during the time when you’re trying to decide whether this game is fun for you. You can always try to daytrade in Jita or grind missions once you have the proper ships, and make your 1B ISK back, buy PLEX, and apply it towards 1 month of subscription later. It’s basically borrowing a month, to be repaid later, so you can avoid the unfun limitations you have now.