You should support Liverpool, watch the 2005 Champions league final. They are a club with great history and pride. They havent won the Premier league in over two decades, but last year they came 4 points short of winning it. The have a great team spirit, there starting eleven can beat any team on there day, they do lack strength in depth, dont have the spending power of Man U and Chelsea. Liverpool are entertainning to watch, they do score lots of goals, and they usually win games the hardway, like going down 3 goals first lol.
Or you could support Arsenal, they havent done too well in recent years, but they have a great young squad and they do play attractive football.
if you want a team out side the top four then perhaps you should look @ the following
Everton, they have a small squad, dont have money to spend, but have some great players and there manager is very good. They are the only team to have broken into the top 4 in the last 10 years, they came 4th in 2005, think that was there highest ever finnish to a season. this year they also reached the FA cup final, it was a shame they lost to chelsea at the final hurdle.
You should support whomever gets the hairs on the back of your neck to stand on end. Whomever has you on the edge of your seat with tension. Be that Accrington Stanley or Manchester United, it doesn't matter.