In the realm of starting mechs, the Uller Prime and the Owens C are the easiest to pilot. The Uller flat out has more firepower than the Owens C, but the all those lasers are easy to pinpoint onto one spot, making a clean shot very rewarding. A fight between the two comes down to how well the Owens C can start circling its opponent, as the longstanding hit detection issues give it quite an edge. If the Uller backs himself against a wall, he stands a good chance of at least drawing out the fight long enough to lay some pain on the Owens.
The Owens B used to be what the Owens C is now. I call them the Roller Derby mechs, people just keep moving in them and never stop to think, because they don't have to. The performance of the Owens B will depend on how much the bugginess of SSRMs affects you. Give it a try, anyhow.
For midrange mechs... yeah, the shadow cat is pretty good, but then all little boys have to grow up sometime and stand the line as a man in a Bushwhacker. The Shadow Cat is recommended because of its speed and maneuverability, which often allows it to hang at the back of the battle. The Bushwhacker, on the other hand, has armor that surpasses some heavy mechs and often some serious firepower to boot. You'll find yourself caught by the enemy quite often, but in a mech like the Bushwacker A (aka "Warthog"), you'll have the serious firepower necessary to push against the odds, which is always a rewarding experience.
Just keep out of the Bushwhacker Prime, and you'll be fine. The UAC10 just isn't a reliable main weapon, and the large laser can't pick up the slack.
Don't disregard tanks, either. They're essentially mobile turrets, so what they have on them is what's going to determine your experience. The Oro is often overlooked because it's compared to the Demolisher, but it can lay down some serious pain and take some as well. The RAC2 Partisan lays down a vicious stream of firepower as well, and you can get it at the second rank.
Mechs that depend on LRMs are not recommended for new people because their success often depends largely on how well the rest of your team is fending back the opposition. Think on the state of the battlefield and how much you're going to need to defend yourself before buying one of these.
As a compromise, the Vulture Prime and Catapult Prime are both support mechs with some ability to support themselves. The Catapult is especially good at anti-camping, as its ELRMs can reach out and touch someone beyond the range of most weapons.