The budget is kind of low. I personally would recommend to spend at least $200 on a subwoofer amplifier. Get something well known for quality amplifiers.. Alpine, JL Audio, Kicker, Boston Acoustics, etc. Now onto subwoofer..
The way I see it, if you like to play your music loud, a single 10 inch subwoofer will choke faster than a comparabler 12 inch subwoofer. A dual 10 inch sub setup will have better SQ (due to lower excursion) and power handling than a single 12, but it will also cost a lot more. So pick your poison..
In terms of what subwoofer to buy.. obviously there are too many brands to be familiar with all of them at once. I personally really like Harman Kardon (JBL/Infinity products). Most of mid-level or better Harman Kardon subwoofers are considered very good: JBL Power series, JBL WGTI, Infinity Kappa. The WGI is considered by some as the best SQ sub.. at any price. All of these will sound good in a sealed box. I personally consider the Kappa to be a sweet sub for a budget setup. Good sensitivity. Great sound in 1cu ft sealed box. Cheap.
Dayton HF12 requires a sealed box that's too big to be considered to be used in car/suv IMO.
Dayton HF10 seems fine, but the output may be limited for bass heavy stuff. It may be just right for rock and country.
Dayton HO 10/12.. IMHO.. these were designed for ported box use. In sealed box, these have pretty bad sensitivity and limited deep bass extension.
Image Dynamics IDQ v3: excellent subwoofer for compact sealed box application. Very good sensitivity and power handling. Expensive.
Peerless XLS: In the same league with Dayton HO (best works in ported box or with passive radiator), but more expensive.
Peerless XXLS: In the same league with Dayton HF (e.g. you need a biggish sealed box). Very good sensitivity. Expensive.
My personal pick for budget setup: Infinity Kappa 120.9w. Very nice and tight sound, and will get pretty loud even in a sealed box.
My pick for "no cost spared" setup: JBL WGTI. Sorry, never heard it, but based on reviews, exactly the sub I dream about..