I had a beer with my supper and started to feel pretty good.
The beer I had with my dinner made me feel slightly intoxicated, but I feel good.
ーI had a beer with my supper and started to feel pretty good.
「夕食にビールを飲んで結構いい気分になってます」
to have a beer with one's supper で「夕食にビールを飲む」
to feel good で「気分が良い」
この言い方でほろ酔いなニュアンスも伝わりますよ。
ーThe beer I had with my dinner made me feel slightly intoxicated, but I feel good.
「夕飯に飲んだビールでほろ酔いだけどいい気分です」
to feel slightly intoxicated で「わずかに酔う感じがする」＝「ほろ酔い気分です」
ご参考まで！
カナダ 
