I've analyzed 50+ properties and most of these do not make any sense at current prices.

You didn't specify if that's gross or net.You might be able to hit 50% of your target (that would be $2K gross monthly income) with what you have.You can target a C- neighborhood and shop for a fourplex property with 2bed/1bath units, bringing in $500 in rents per unit.Your price target would need to be <= $120K.

This property barely meets the 1% rule, but this is common in this area.  

210 - Bastrop 1 - Aldine 2 - Alief 3 - Alvin 135 - Anderson-Shiro 4 - Anahuac 5 - Angleton 215 - Belton 111 - Austin 6 - Barbers Hill 136 - Bellville 132 - Bay City 181 - Chester 143 - Beaumont 140 - Boling 150 - Brownsboro 54 - Brazos 7 - Brazosport 128 - Burton 144 - Brookeland 137 - Brenham 66 - Cayuga 8 - Channelview 9 - Clear Creek 100 - Cleveland 101 - Coldspring-Oakhurst Consolidated 10 - Columbia-Brazoria 141 - Comal 148 - Bryan 176 - Devers 177 - Yoakum 169 - Calhoun County 204 - Fayetteville 184 - Burnet Consolidated 194 - Buffalo 11 - Conroe 118 - Coupland 57 - Crockett 12 - Crosby 13 - Cypress-Fairbanks 180 - Wharton 155 - Centerville 14 - Damon 15 - Danbury 202 - Franklin 74 - Dayton 16 - Deer Park 112 - Del Valle 197 - Ezzell 189 - Giddings 153 - College Station 179 - Hallettsville 17 - Dickinson 119 - Dripping Springs 113 - Eanes 18 - East Chambers 145 - East Bernard 120 - Elgin 68 - Elkhart 19 - Fort Bend 67 - Frankston 20 - Friendswood 21 - Galena Park 22 - Galveston 23 - Goose Creek 138 - Goodrich 58 - Grapeland 59 - Groveton 110 - Hamshire Fannett 107 - Hardin 121 - Hays Consolidated 24 - Hempstead 25 - High Island 26 - Hitchcock 27 - Houston 28 - Huffman 108 - Hull-Daisetta 29 - Humble 64 - Huntsville 139 - Kerrville 175 - Madisonville Consolidated 170 - Matagorda 185 - Keller 186 - Lufkin 187 - Jarrell 205 - La Grange 183 - Llano 217 - Hemphill 106 - Jacksonville 122 - Johnson City 198 - El Campo 30 - Katy 60 - Kennard 218 - Nacogdoches 159 - North Zulch 178 - Lockhart 32 - Klein 35 - La Porte 69 - La Poynor 114 - Lago Vista 200 - Laredo 115 - Lake Travis 33 - Lamar Consolidated 61 - Latexo 123 - Leander 73 - Liberty 149 - Jasper 151 - Leggett 103 - Livingston 62 - Lovelady 154 - Lumberton 36 - Magnolia 116 - Manor 124 - Marble Falls 37 - Montgomery 70 - Neches 129 - Navasota 38 - Needville 39 - New Caney 105 - New Waverly 152 - Nederland 195 - Leon 196 - Mexia 131 - Normangee 127 - Northwest 104 - Onalaska 99 - Other 71 - Palestine 126 - Rockdale 41 - Pasadena 42 - Pearland 117 - Pflugerville 125 - Round Rock 207 - Schulenburg 44 - Royal 45 - Santa Fe 109 - Sealy 46 - Sheldon 65 - Slocum 130 - Shepherd 47 - Splendora 48 - Spring 49 - Spring Branch 50 - Stafford 206 - Round Top-Carmine 51 - Sweeny 102 - Tarkington 52 - Texas City 133 - Tidehaven 156 - Palacios 147 - Rusk 219 - Waelder 199 - Marlin 53 - Tomball 63 - Trinity 134 - Van Vleck 55 - Waller 72 - Westwood 56 - Willis 216 - Woden 142 - New Braunfels 188 - Columbus 190 - Rio Vista 192 - Snook 157 - Seguin 158 - Somerville 161 - Rice Cons 182 - West Hardin 203 - Weimar 220 - Salado 214 - San Marcos 193 - Nueces-Canyon 160 - Lake Worth 162 - McDade 164 - Big Sandy 165 - Lexington 191 - Victoria 163 - Hardin-Jefferson 208 - Denton 209 - Caldwell 211 - Dallas 201 - Wylie 168 - Zavalla 171 - Iola 213 - Richards 221 - Buffalo/Lone Star

I have 4 rental properties.  1 has about 50% equity. 

I would be pre-approved for about 280k and I make around 40k a year so I'm not sure what 15k would get you.Having the money ready for down payment and closing costs is excellent and would be a point in your favor for sure.Also, an option you can consider is having someone else be a co-borrower but in this case they would also have to follow the FHA rules I believe.

Couple of rules to implement: no pets, no significant others staying over more than a weekend's time, no mini fridges or heaters.

Two of the units are under rented by at least $50 if not $100, but those two units could use a refresh.

Two of the units are under rented by at least $50 if not $100, but those two units could use a refresh.

According to Corelogic , almost half of top US housing markets are 'overvalued"---At the end of July, of the top 50 markets, based on housing stock, 46 percent were overvalued, according to CoreLogic.