Their are many wallet available in the market. For desktop wallet I would suggest you the bitcoin core. Bitcoin core is the first and original wallet. It is safe and secure but it required lot of space upto 65 GB. another is multibit. It requires only 30 MBs so you can use that. Talking about mobile wallet mycelium.mycelium is one of the safest and recommended wallet. you can surely go for mycelium. If you want online transection then you can go with bit go, green address. Hope it will help you