The 2008 Specialized Allez Elite (compact) is pretty much full tiagra with a 105 rear derailleur. The tiagra group is 9 speed. The 105 group is 10 speed. If you plan to go to 105 get a bike with 105. A 105 group costs roughly $550. Not something you want to add to a brand new bike. Decide if 9 speed Tiagra is fine or you want a bike with 10 speed 105. There is nothing wrong with 9 speed or with tiagra. They both work fine.
Now once you figure that out here are some recomendations (these are the most popular things you cant really go wrong with).
You need something to repair flats on the road and a way to hold it.
- Get a saddle bag. Topeak Aero Wedge is most popular. Small for bare minimum, medium for average amount or large if you hold more then average.
Then you have to fill the saddle bag. Get a tube patch kit and a tube. Tire levers (park tool plastic set of three or similar). A co2 inflator. Genuine Innovations makes good stuff like the Ultraflate, Microflate, Ultraflate2 ect... If you dont want co2 and want a frame pump Topeak Road Morph G is the unofficial best pump.
Now you will be thirsty when you ride. You need bottle cages and bottles. Best overall are the Tacx Tao cages. They are light, look good, and will hold any bottle without it flying out. There like $15 each. And get any bottles you want for them.
Pedals for the bike. I prefer Shimano SPD-SL pedals. A good pedal is the 105 level pedal. (PD-5600 I think). And then you need shoes for them. Thats where it could get expensive. Sidi Genius 5 are very popular. (roughly $229). Good if you have wide feet bc they have a wide version. Otherwise go to your LBS and try on some cheaper shimano pairs. Whatever feels good will be fine.
Computer. Cateye Astrale 8 is a very nice cheap computer that does it all. Has cadence too (RPM). The only downside is it is wired (A wire runs to the back wheel). Not really a bad thing but some dont like the look. If you want wireless the Cateye Strada Wireless is very popular. The thing is it doesnt have cadence. If you want wireless and cadence that is when they start to get expensive so its your choice.
Clothing. For a jersey you can get a cycling specific one or you can get something similar to underarmor. The benefits of cycling specific ones is they have pockets in the back to hold food, tools, phones, ect... and they have a zipper if you want to open it up a bit. You dont necessarily have to spend a ton on a jersey. As far as "bottoms". You have a choice of shorts or bibs. bibs have suspenders. bibs are liked more then shorts by most people for their additional comfort and lack of butt crack hanging out. Dont cheap out on shorts.
Just another thing to keep in mind is the accessories add up very fast. Dont max out your budget on your bike and not be able to afford the additions you need to go with the bike.
Just my opinion. some others will recomend different parts but these are pretty common and popular.